Many stories will have animosity between a beautiful, highly advanced race or civilization, and a much more gritty, industrial, technological force (note: "technological" in the sense of having a non-religious attitude toward their tech, in the literal sense both civilizations tend to draw on the same magical or technological forces, making them Not So Different). This theme of Harmony Versus Discipline and Romanticism Versus Enlightenment is very common, regardless of the genre. Also look at the Apollonian/Dionysian contrast.
In many fantasy fictions these roles are filled by Elves and Dwarves. Elves are tall and slender, Dwarves are short and stout. Making a physical difference like this is a common way to point out that the two groups are meant as a foil of one another.
Elves use swords and bows, weapons requiring flexibility and precision, representations of elegance. Elegance is power. Dwarves use axes, hammers and crossbows, which are primarily about direct (or in the case of the crossbow, mechanical) application of force. Strength is power.
Elves will focus on magic and spirituality and evince disdain for material things, or to be more interested in their elegance than their utility. Beauty is strength. Dwarves will sometimes use muskets or revolver-style pistols and various Steampunk machines and tanks, all representations of industrial, technological might. Innovation is strength.
Elves live in pristine woods, crystal spires or elegant palaces, emphasis on light and natural beauty, openness. Dwarves live in great halls and impregnable fortresses that are usually underground, emphasis on artifice and containment.
Elves dress fancily, sing elaborate songs, write poetic literature in flowing script, and are embodiments of beauty and style. Dwarves are often unkempt, sport long beards and hairs, and dress in either simple leather, undyed wool — or steel — and write prose in runes, carved into the rock.
We've given a lot of information here about the specific races, Elves and Dwarves, but the core of this trope is not about them. It is about how that plays out in lots of stories that have no Elves or Dwarves in them at all. In historical fictions/fantasies you will find Aristocrats versus Barbarians, for example, which could be exchanged for Elves and Dwarves quite easily. Science Fiction will have some variation on Eloi and Morlocks, or a Crystal Spires and Togas race versus Humans, or a primitive but nature-oriented race versus Humans. In a contemporary business setting, it will be Marketeers versus Engineers. A lot of the modern retelling of the classic Cowboys and Indians western sagas has been presented as this sort of "spiritual barbarian vs. industrialized civilization" meme. Force And Finesse tends to describe their contrasting combat styles.
A common subversion is for the Elf and the Dwarf to better understand each other and their respective cultures. The Dwarf may gain a new respect for the Elf's culture and deep learning, while the Elf comes to appreciate the Dwarf's craftsmanship and hard work. Also expect both sides to put aside their differences and team up against a third enemy. That third enemy is usually portrayed as primarily destructive (Orcs, for example). The attribute shared by elves and dwarves primarily being creativity.
Compare with Pirates Versus Ninjas — although the latter is a recent Memetic Mutation while this trope is Older than Television. Likewise the horror-oriented werewolves vs. vampires. Comedy will show this one as Slobs Versus Snobs, Big Guy, Little Guy, or Fat and Skinny. It can sometimes manifest as a form of Fantastic Racism. Don't expect to see a dwarf/elf hybrid due to Hybrid Overkill Avoidance and both sides being verysquicked at the prospect.
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Averted in Queen's Blade with Ymir, the dwarf princess, with the elves, who befriends a lot with them, as long she doesn't try to sell steel weapons to them, since it's implied to be forbidden for them to use those weapons.
Record of Lodoss War makes good use of this trope in playing up the initial dislike between the aged, bitter dwarf Ghim and the flighty elven princess Deedlit. Character Development leads them both to understand the other better.
In James Cameron's Avatar, the Na'vi are amazing natural archers, have a deep empathy for their environment, are not ones to really mess around, and are tall, slender, and lacking in body hair. The Humans are incredibly skilled at craftsmanship, construction, and engineering, utilize big guns, mining machines, and high impact weaponry, live in dark multi-layered cities with lots of technology and little vegetation and natural light, mostly lack a spiritual connection with their world, and are rather gung-ho and upfront, not to mention short, stocky and hairy, when compared to the Na'vi.
The classic silent film Metropolis has a leisure class living above ground in luxury, while workers both live and work below ground.
The 2012 film adaptation of The Hobbit plays up the animosity between elves and dwarves. Thorin hates elves because they wouldn't help fight off Smaug when he came to the Lonely Mountain.
The climax of Return of the Jedi is a classic IN SPACE! example with our heroes being aided by the Ewoks—basically a race of teddy bears with primitive weapons—against the empire, with its technologically advanced arsenal.
In some variations of tradition The Fair Folk are beautiful but erratic and dangerous possessing strange powers of enchantment. Mortals are more ordinary and depend on tools and organization.
Both played straight and subverted in the Fighting Fantasy gamebooks, depending on where exactly you go in the world of Titan. It's noted that many dwarves and elves really don't get along, but it tends to be more due to misunderstanding rather than outright antipathy. The subversion comes when canon also notes that there have been several notable adventuring team-ups between elves and dwarves, and both races have a certain respect for the love the other has for nature/the earth. The Zagor Chronicles series of standalone novels further fleshes out this trope when the dwarf Kagand explains to the dwarf Stubble (who comes from another world) that, while dwarves and elves have slain enough of each other in wars over the centuries, they actually live in harmony in places like Darkwood. This is a mild form of culture shock to Stubble, as the dwarves and elves on his own world have a deep-rooted dislike that goes back centuries.
Older than Television: H. G. Wells' 1895 The Time Machine features the Morlocks (below ground, industrious) and the Eloi (above ground, beautiful, musical), two (sub?)-species of humanity, in the year 802701. Unlike the more common form of this trope, however, the Eloi are neither highly advanced nor highly intelligent. Indeed, they're little more than the Morlocks's purebred humanoid cattle.
Although they hadn't come to blows in a long time, Elves and Dwarves had a lot of distrust towards each other in The Lord of the Rings. It originated mostly from an ancient war between the dwarven city Nogrod and the elven kingdom Doriath which destroyed both nations; and also from a general severing of ties between all the races that made them much more isolated and thus suspicious of each other. Character Development subverts this in the case of the elven Legolas and the dwarven Gimli, who both come to understand each other better and become Friendly Rivals, then Heterosexual Life-Partners.
Tolkien's The Lord of the Rings is also likely the source for this trope. Tolkien set many standards which have made their way into modern fantasy, especially after being further popularized by other pop culture phenomenon such as Dungeons & Dragons. Prior to Tolkien's work elves and dwarves were not usually seen as being distinctly separate kinds of beings in most mythology. Often they were synonymous with other fey creatures who inhabited either the woods or the water or mountains. Tolkien created different categories for these beings and made them more humanoid than they were previously in mythology.
Codifier for modern use and supplier of the actual terms "dwarf" and "elf", yes, but not source of the trope in general. Tolkien pulled the "tall, slender fae who hang around doing their own thing" vs "short, muscular fae that build stuff, mine, and interact with humanity to sell their awesome stuff" cultural rivalry pretty much straight out of Norse Mythology, specifically the Eddas, and corresponding Celtic and Germanic lore. It's older than steel, probably.
Even in Middle-Earth the Elves and the Dwarves got along fairly well at times despite not always really understanding each other. Eregion and Khazad-dûm come to mind; the gate between them allowing entrance to the Dwarven kingdom opened to the word "friend" spoken in Elvish. It was apparently intended as primarily symbolic (or to keep out weather and animals), not as an actual obstacle.
The Sword of Shannara is highly derivative of Tolkien (later books in the series are less so), but his elves and dwarves get along quite well and have for centuries, thank you very much. Also, Brooks' dwarves have a morbid fear of being underground, to the extent that a given a choice between sleeping outside in the rain and sleeping in a cozy, dry cave, the typical dwarf is going to wake up wet.
Averted in The Chronicles Of Thomas Covenant The Unbeliever where Stonedowners and Woodhelvinnen don't have much of a problem with each other in the first series. Of course, they're genetically identical and part of the same nation/culture; they just live in different places and make tools primarily out of the available indigenous materials. In the second series they don't get along so well, but then in the second series everyone outside your own village is at best competition for all-too-scarce resources.
In Katherine Kerr's Deverry novels, many of the Mountain Folk (dwarves) believe the Westfolk (elves) are all thieves, and enchant their weaponry to glow when they come into contact with elves (this is how it's revealed the main character is a Half-Human Hybrid). Any antipathy the Westfolk have to the dwarves is mostly a reaction to this attitude.
Averted in Raymond E. Feist's Riftwar Cycle, where Dwarves and Elves are on the whole pretty good friends. They even get along fairly well with humans, and both races have a Worthy Opponent thing going with the Dark Elves.
In the Timothy Zahn book The Green And The Gray the two races, Greens and Grays, are basically Elves and Dwarves respectively and yes, they've been at war for centuries.
Played with in three of the worlds from The Death Gate Cycle. In Arianus, the Elves are The Empire and the Dwarves are an oppressed slave race that serves them; in Pryan, the Dwarves generally don't like anybody, but there doesn't seem to be any particular animosity between them and the elves; in Chelestra, the two races are shown to be staunch allies who may indulge in mockery of each other but have great respect for each others' abilities.
Also in the Star Trek Novel Verse, the rivalry between Huanni and their offshoot race the Falorians. Huanni are graceful and ethereal as well as emotionally expressive, Falorians are stockier, stoic, disciplined and historically a labour class.
The Elves and Dwarves in the Inheritance Cycle add another twist to this: the Elves are generally very scientific, while the Dwarves are religious. Note that this has nothing to do with technology: the series is strictly "swords & sorcery." But for example, the Dwarves worship Stone, believing that they came from it and return to it in death, and one of their priests mentions why they know that stone is alive: coral reefs, which grow over the decades. The hero is suitably impressed with this, until he meets the agnostic Elves who posit that there is no evidence supporting any gods or supernatural beings, and that the coral are just the accumulation of billions of tiny dead sea creature fossils.
In a series set technologically in the Medieval era, magic is the only way to properly study the world. A particularly meticulous king of a small nation is overjoyed to have a few of rebels' mages at his beck and call, being suddenly able to really study the world in detail.
Subverted in a short story from Dragon, in which a dwarf community built under a gigantic tree is revealed to be even more spiritually attuned to the tree than the elves who worship it on the surface. The dwarves tend its roots with loving care, and are grateful to it for holding the roof together and guiding them to water. When it gets sick, the elves just worry about what its illness forebodes; the practical-minded dwarves seek out and correct the problem with the tree's taproot.
Randy Waterhouse in Cryptonomicon by Neil Stephenson divides the world into Elves (ingenious, calculating and highly motivated people, like his business partner Avi), Dwarves (hard-working "plodders," like himself), and Men (everyone else outside the realm of nerds that he inhabits).
Subversion of this in R.A. Salvatore's The Cleric Quintet and some of his later Drizzt novels, which feature Pikel, a rather eccentric dwarf (he dyes his beard bright green) whose ambition in life is to become a druid (to the sheer horror of both the elven monks he goes to for training and his brother Ivan, who is the epitome of everything blunt, earthy, and dwarvish). However, Pikel's affinity for nature and his druidic abilities eventually end up creating quite a rapport between certain dwarven and elven settlements.
Drizzt himself is a subversion as a dark elf who befriends a dwarf chieftain, Bruenor Battlehammer.
In the Discworld book Soul Music, Glod the Dwarf acts a bit hostile to Imp at first when he thinks he might be elvish.
Also in Lords and Ladies, it is mentioned that dwarves and trolls would kill an elf on sight, but for a good reason. Discworld elves are somewhere between Nazis with magic and demons with good PR.
Dwarves and trolls are hereditary enemies. Dwarves mine, which involves smashing rocks to get valuable minerals out of them, and trolls are basically animate rocks with valuable minerals in. This despite the fact that both races are Stout.
This runs all through the Green-Sky Trilogy, despite the fact that the Kindar (willowy, pale, overly-diplomatic, tree-dwelling vegetarians) and Erdlings (stocky, Ambiguously Brown, plain-spoken, underground-dwelling hunters) are simply two separate human cultures.
Essentially there in Julian May's Saga of the Exiles with the Tanu and Firvulag. Tanu are tall and beautiful, while the normal Firvulag is short and stocky, although their heroes can be equal or better than the Tanu.
In Sevenwaters Trilogy the Sevenwaters clan are in touch with nature and nature spirits, while the Northwoods are stodgy folk, and more settled in mentality.
The Billibub Baddings books, which features a dwarf from a Standard Fantasy Setting being stranded in Chicago in the late 1920s, alludes to and lightly parodies the rivalry between elves and dwarves — though the dwarf protagonist certainly doesn't hate elves (especially not the women!), and in fact reveals that in their world, the rivalry originally started over a recipe for malt beer.
A Song of Ice and Fire has the Children of the Forest and the Race of Men. Men can also be divided between the sly and elegant Southrons and the straight talking and brutal Northmen.
Ironically, the cultured, urbane, "advanced" Free Cities and the "barbarous" Proud Warrior Race Dothraki coexist relatively well. The Dothraki show up and rattle their spears, and the Free Cities bribe them to go away because it's cheaper than hiring mercenaries to run them off. Diplomatic relations are strong enough that Illyrio can invite Khal Drogo and seemingly his entire khalasar over to discuss a marriage pact with few or no problems.
"The Cloud Minders" had graceful and scholarly humanoids living in a literal flying city, while brutish and mentally limited miners dug tunnels with simple hand tools underground. It's later revealed that the two are actually the same species, but the miners are exposed to a mineral that affects the brain.
In the episode "Journey to Babel", Vulcans and Tellarites have a classic elf-dwarf relationship, with Sarek of Vulcan a rather witty Legolas and Gav the Tellarite a doomed variant of Gimli.
Bajorans and Cardassians have a sort of dark elf/drow and dark dwarf enmity going on.
The long-standing rivalry between the haughty, arrogant but unfailingly cautious Romulans and the Proud Warrior Race Guy Klingons.
The Federation versus the Borg. The Federation is enlightened, utopian, and based on the principles of personal freedom and self-determination. Their technology is elegant, aesthetically pleasing, and geared largely toward improving quality of life. The Borg are single-mindedly dedicated to forcing the entire universe to conform to their ideal of "perfection," which is total submission to a plague-like rapacious Hive Mind. Their technology is ugly, industrial, but functional; they have no real sense of aesthetics or artistic creativity, and no purpose other than to consume and expand.
In Babylon 5 Minbari are elegant, traditional, and warriorlike fighting in a heroic fashion. Humans are practical, mechanistic, and soldierlike fighting in a militaristic fashion.
Meanwhile the Centauri are decadent, pompous,and huge consumers of art and culture, and the Narn are brutal, Hot-Blooded, and weapon mongerers. It is indicated that the Centauri made them that way when they enslaved the Narn, however. Finding common ground to settle their differences is a major background plot for much of the show, culminating in them forming a temporary alliance along with the Minbari and the League of Nonaligned Worlds to help Sheridan liberate Earth from Clark's dictatorship.
Played absolutely straight in the Warhammer fantasy battle game. The Elves and Dwarves carry residual hatred from the War of the BeardWar of Vengeance that they fought long ago. The Elves are magic-wielding Imperialists, while the Dwarves miner-industrialists with relatively advanced technology (including firearms, cannons, and steam-punk helicopters). The conflict resulted because of the Dark Elves framing the elves for attacking a dwarven caravan, and the High Elven king at the time being a complete moron who had the dwarven emissary shaved, a dire insult to dwarves. So in a world where the forces of Chaos constantly threaten to overcome the world, naturally they went to war against each other. At the end of the war, several thousand on both sides were dead, the elven king was killed by the dwarves, etc. The elves won't forgive the dwarves because they won't return his crown, and the dwarves won't forgive the elves because dwarves keep a great big book where they write down every act anyone's ever done to annoy them, just to make sure they don't stop being mad about it. Incidentally, they have stated that they will return the crown if the elves pay reparations for the original insult and the expenses involved in the multi-generation war to collect.
It's Eldar Vs Humans on a galactic, genocidal scale in Warhammer 40,000, with the Imperium of Man squarely filling the dwarves' shoes. Though in this case, it's less about swords and bows vs axes and hammers than it is starcannons and hovertanks vs chainswords, battle cannons and heavy, tracked monstrosities.
Since both dwarves and elves are standard hero races, they tend to be on decent terms, though usually not seeing eye to eye on much (typically more like eye to groin). The 3rd edition rulebook mentions that while dwarves and elves don't always get along, if one gets attacked the other will be the first to help them. Much like brothers. This was less the case in the 1st Edition, where the table for racial relations explicitly noted that dwarves and elves had a noted antipathy towards one another. Humans generally tended to be regarded neutrally by all the demihuman races.
Eberron has a really weird version of this between the halflings of the Talenta Plains and the elves of Valenar. Thing is, it's the halflings standing in for the elves in this trope - primitive, spiritual, attuned to nature, and generally cleaving to the Magical Native American idea, only they ride dinosaurs. The Valenar elves, in turn, stand in for the dwarves, being accurately described as land-based Vikings. The actual dwarves of the setting are geographically removed from both races and thus are neutral towards both.
In the Iron Kingdoms setting (where WARMACHINE and HORDES are set), the highly-industrialized titular Iron Kingdoms (the WARMACHINE factions) often find themselves at odds with the much more naturalistic Primal Powers (the HORDES factions). Of course, there's plenty of infighting among the Iron Kingdoms and the Primal Powers as well. Notably, this trait is actually averted by the setting's actual elves and dwarves, as the elves are rabid xenophobes who hate everyone, and the dwarves, while isolationist, are on generally friendly terms with all the other races.
Added to said avertion the Elves and Dwarves use to be fairly good trading partners.
The Jadeborn (with a hint of elfish traits) and The Fair Folk in Exalted don't exactly meet often enough to develop an attitude about it, but their very natures are inimical to each other — the industrious, inventive Jadeborn being about as close as you can get to representations of Creation and Order without being an Earth elemental, and the alien Fair Folk being a tiny piece of Primordial Chaos that for whatever reason decided to pretend to be sentient and go around Mind Raping people.
Within the Jadeborn society, the Artisan Caste (the most elf-looking) are typically prejudiced against the Worker and Warrior Castes, regarding the regulars as uncouth and brutish and the Enlightened ones as freaks and upstarts, while the other two Castes deride the Artisans as stuck-up, arrogant and a little bit crazy.
In The Dark Eye, elves and dwarves have some issues, (see that article for a more detailed list).
The gods of Asgard (Elves) vs. the Nibelungs (Dwarves) but also the giants (Fasolt and Fafner) in The Ring of the Nibelung by Richard Wagner. Alberich in particular is often interpreted as an embodyment of Capitalism, out to depose the old, feudal elites.
In Knights of the Old Republic, the Echani and the Mandalorians. Both are a form of Proud Warrior Race Guy, but they go about it in different ways. Echani are famous for their graceful combat and finely crafted light armor and weapons, whereas the Mandalorians are well known for their powerful heavy armor and fondness for big, heavy, sturdy weapons. One memorable conversation with a Mandalorian mercenary on Manaan has him pegging the Echani as "Fey dancers wielding flimsy toy weapons not suitable for mandalorian children." The Echani are also regarded by many fans as physically elf-like for their lithe bodies and their features.
In Mabinogi, the elves and giants are at war. You never see any actual raiding, aside from reminiscences, but any elf or elf-aligned human in the giant village will be attacked on sight by the guards, and vice versa. There is also an option toggle that will cause any character of the opposing race with the same option enabled to be targeted and attacked like a monster. However, the elven healer Atrata and the giant blacksmith Taunes are old friends, suggesting that the war is not built-in.
Of course, Mabinogi giants are basically dwarves in every respect except for actually being short.
Scribblenauts has a classic example. While an ordinary "Elf" is no trouble, try putting a "Wood Elf" and a "Dwarf" next to each other. If both unarmed, the dwarf panics and is slain by the elf. If both equally armed, the dwarf will defeat the wood elf.
The dark elves of the series, Dunmer, are described as a traditionalistic, religious, racist, proud bunch. Some of them were also quite backstabbing, vicious, and nomadic, though that dependent on which house or tribe they belonged. They lived either out in the fields in tents for the tribes or preferred lavish houses grown via magic from super-mutated mushrooms and vines. The race of technology-minded "dwarves", the Dwemer, had all suffered a Critical Existence Failure after messing around with a Cosmic Keystone long before even the first game in the series so we know little about their nature directly, but their method of lifestyle is well-documented in subterranean Steam Punk cities that repair themselves via a continuous automaton skeleton crew and security (which, notably, is a combination of both science and magic).
The Dunmer and Dwemer did play classical Elves versus Dwarves diplomacy up the point the Dwemer disappeared: generally at loggerheads, but quite willing to bury the axe and work together when a greater enemy showed up.
Amusingly subverted: according to The Elder Scrolls lore, any race that has "-mer" in its official name is descended from an ancient Elvish race called the Aldmer. Also, the Dwemer weren't that short...
The Elder Scrolls case is more of a subversion. The "dwarves", while seemingly atheist, they were a very spiritual people - so much that the aforementioned Critical Existence Failure happened in an attempt to become gods themselves. Both of them also base their technology on magic - the Dwemer even more so than their neighbours.
While the Dunmer/Dwemer case is more of a subversion, this trope is played straight with the human Empire playing the dwarves to the Dunmer elves.
Played horrifically straight with the Dwemer and the Falmer. During the Merethic Era, the Ancient Nords and Snow Elves went to war, eventually leading to the Snow Elves nearing extinction and forced to seek refuge underground amongst the Dwarves. However, they were betrayed and enslaved by their brethren and twisted and mutilated into a slave-race. Nowadays, the Falmer exist as Morlock-like monstrosities, leaving them blind, feral and barely sentient.
In the game Arcanum: Of Steamworks & Magick Obscura this is mildly subverted. Dwarves and Elves don't particularly understand each other, but they aren't enemies... except that this misunderstanding was exploited by the Dark Elves, who got the Dwarves to banish one of their own clans for the humans' destruction of an "elven" forest. Culminates in a rather interesting (which has several opportunities to never be seen) conversation between Loghaire Thunder Stone (king of the dwarves) and Z'an Al'urin (a True Neutral Dark Elf), which humbles Loghaire but-quick.
The elves and dwarves (and gnomes) of Majesty won't settle in your kingdom if any of the other races are present. While the dwarves here are depicted as typical 'gruff engineers' the elves are far from mystical, magical, or wise, but are instead a bunch of hedonistic layabouts who bring vice to your city in the form of gambling halls and elven lounges. On the plus side, elves effectively double your income.
Subverted in one mission in the expansion pack, when you find yourself assisting refugees from a war between the elves and the Greater Gorgons. If you last long enough, the second wave of reinforcements is a large party of dwarves.
Stonekeep features dwarves who are prejudiced against elves. And goblins. And trolls. And fairies. And various other green-skinned races. And dwarves who have been dishonored. Despite all this, the dwarves are not unlikeable, probably because they have no problems with humans whatsoever. Dwarves make up the majority of your traveling companions early in the game, and one does nothing to hide his intolerance of party members from the above races.
The story of the NES game Faxanadu revolved around Elves vs. Dwarves, although it's because the dwarves had gone psycho and turned into demons.
In Overlord, it turns out that - a short while before your Awakening - the Dwarves and Elves fought a war of extinction. The Dwarves won, carting away the most valued treasure of the Elves, as well as several cartloads of elven slaves to work in their mines, and leaving the Elvish forest of Evernight to the mournful whispers of the ghosts. If you are so inclined, you can help the Elves regain their freedom, and their treasure... or you could kill them all and keep the treasure to yourself. Canonically the Overlord saves the Elves from extinction since they're still around in the sequel while the Dwarves are presumably devastated by the magical Cataclysm that turned the lands of the first game into a magical wasteland. The prequel Overlord: Dark Legend has Lord Gromgard, the previous Overlord instigate a war between the Elves and Dwarves by killing their leaders and framing the other side for it.
Subverted in The Legend of Zelda: Twilight Princess, when the Gorons seem to hate the Hylians, but actually the Gorons were just ashamed for having problems with an evil curse on their leader, which is why they kept the Hylians away from their territory.
In Class Of Heroes, Elves and Dwarves don't get along with each other, thus making it harder for them to gain affinity points when characters of both races are in the same party.
Averted in Age of Wonders. The dwarves and elves are ancient and steadfast allies, especially against the human invasion. Nevertheless, the default relation between the two races is "Polite" (one step below the best, which is "Friendly").
Much more directly lampshaded, and laughably subverted, when Oghren is in the party when you recruit Zevran:
Oghren: We're taking the elf?! Oh, fine, fine. I see standards are just falling down all over the place.
Zevran: I see. Are we now supposed to engage in some manner of archetypal dwarf-elf banter, my friend?
In Dragon Age II, Varric and Fenris are relatively cordial to each other. While Varric is one of the few party members that remains on good terms with everybody, Fenris is generally antisocial and quite antagonistic towards the other members, particularly the mages (or at least the ones that aren't Hawkes). Varric adores Merrill, the party's other elf, nicknaming her "Daisy" and treating her like a little sister.
The relative lack of animosity between the two races probably has to do with the fact that they never really interact much. The elves are too busy recovering their history and avoiding being killed by the humans, and the dwarves are too busy recovering their history and avoiding being killed by the darkspawn...and themselves.
Noticeably absent in Mass Effect. The Asari are a fairly easy Elf equivalent, but there isn't really a clear Dwarf race. The best fits would be the very militaristic and civic-minded Turians, but they were invited to join the Council because of their military prowess & there's no history of major dispute between the two races. Or the Batarians, but they're more like intelligent Orcs or barbarians. And they don't really like anybody.
The Krogan fit the Dwarven mould rather well, being militaristic, blunt-spoken and their homeworld is the remains of a heavy industrial civilisation, destroyed by nuclear war. However, due to sharing a lifespan that lasts over a thousand years, it's mentioned that Asari/Krogan relationships are somewhat common, making this an aversion of the trope.
A better comparison would be Krogan/Salarian, Salarians being fay, slight, short-lived double talking intellectuals who rely on precision over brute strength. This rivalry is fierce, the Krogan openly despising Salarians and the Salarians engaging in some blatant racism even from sympathetic examples.
To a degree in Kingdom of Loathing; as part of a quest you can start and stop a war between the nature-loving hippies and the beer-drinking frat boys.
The first three games avert this, as elves and dwarves are parts of the same faction. However, the dwarves join the Academy in the fourth game, and gain their own faction in the fifth. Ufretin, the dwarf leader who arranged the rift between the elves and dwarves and the dwarves' integration into the Academy, did so because he felt the chaotic ways of the elves were too much at odds with the orderly ways of dwarves. Similarly, the centaurs, who had been allies of the elves in the previous game, join the Barbarian faction in IV; Tarnum comments that he wondered why the centaurs maintained an alliance with elves for so long, given their aversion to magic.
The dark elves and dark dwarves of the old verse were unfriendly to each other. This may have more to do with the consequences of one race (the Elves) being enthusiastic traders and the other being xenophobic allies/servants of the Earth Elementals than this trope, however (certainly, the dark elves can only barely be said to fit the Elven archetype used in this trope).
Even though Thief has humans as the only civilized race, aspects of this trope show up in the rivalry between The Hammerites, whose religion embodies the concepts of order, technology and civilization, and the paganistic worshippers of The Trickster, whose religion embodies chaos, nature and magic.
Averted in Popful Mail with elven bomb-maker Slick and dwarven artisan Glug, who are the best of friends.
The Elves, who represent the element of Life, and Dwarves, who worship the element of Earth, typically begin with poor relations in Lords Of Magic.
While both factions in Rift have elves, it's the faction that doesn't have dwarves in which this rivalry gets obviously played out: The Kelari elves are not on the best of terms with the bahmi (the imposing, blue-skinned, and decidedly non-dwarven stouts of the Defiant faction).
There's a notable aversion in the form of Cacame Awemedinade, who somehow became the dwarven king despite being an elf. He's the only elf the Dwarf Fortress community holds in high regard, not least because he once killed a dragon singlehandedly.
Averted in the Warcraft games. In Warcraft II and III, High elves and Bronzebeard dwarves went along well, and Wildhammer dwarves were very good friends with the former. Dwarves in general don't seem to have any problem with Night elves, and if they are enemies of the Blood elves it's only because the latter joined the Horde (their rival faction) or the Burning Legion (who are enemies to everybody).
There are some individual examples, however. Tarenar Sunstrike and Gidwin Goldbraids in World Of Warcraft's Eastern Plaguelands have a rivalry very reminiscent of Gimli and Legolas. Likewise, a night elf and dwarf in one of the Warcraft: Legends manga were verbally at each other's throats all the time.
The Alliance's ambassador to the blood elves (before they joined the Horde) was a dwarf, which you would think was an intentional aversion of this trope. Turns out, he was investigating things where he didn't belong and handing off blueprints of arcane sanctums to the night elves hiding in the area.
There is a bit of this trope in Cataclysm, with the dwarven Explorer's League coming to blows with the elven Reliquary.
Lacking any actual elves in the setting and with the dwarves virtually extinct as of the first game, Guild Wars 2 has an excellent parallel in the conflict between the ancient, civilized, beautiful, magically gifted humans and the brutal, industrious, and militaristic Charr, where the humans are in serious decline and are in very real danger of extinction and the Charr are thriving. They're reluctant and wary allies in the game, courtesy of the de facto ruler of the Charr being unusually progressive and far-sighted (who also wants the traditional marker of the true leader of the Charr, which the humans stole centuries back), while the human queen has more than enough trouble on her hands without the Charr.
Lampshaded by descriptions of items in Dungeons of Dredmor, where there was such a war outside the dungeon.
The Witcher is all over the place with this trope. Elves and dwarves don't like each other at all. However, both elves and dwarves are members of the local Anti-Human Alliance called the Scoia'tael. However, there are several dwarves who don't like the Scoia'tael (who, for all their high-sounding rhetoric, are most likely "freedom fighters" In Name Only) and point out that the elves didn't stop being condescending and hateful towards dwarves until human supremacy was already a fact and that the Scoia'tael will always put elves before dwarves. Elves, on the other hand, dislike dwarves mostly because they have had a far easier time being accepted into human society and have managed to preserve much more of their culture and traditions.
In Drowtales, the Light and Dark elves were no longer able to survive on the surface and fled into the depths of their world. There they were faced with hordes and entire cities of dwarves who were none to happy about these new refugees and a war broke out... Which the dwarves lost entirely, whole cities slaughtered and their race pushed back to the barely habitable edges of the underworld. Now they are viewed as a passing pest and nuisance by the elven races and almost all small fights with them end in a one sided massacre by the elves.
The grudge is mostly explained as elves really, really disliking all the beards. Or, to be more specific, both races believe they rightfully own the Earth Orb. Notably not present in the game it's based on, however, which portrays the dwarves and elves as being friendly with each other.
Keeping with the tone of the comic, the rivalry is turned Up to Eleven with both sides gladly committing genocide on the other. The two biggest Sociopathic Hero-protagonists do their part since Thief is an Elf and Black Mage... just enjoys destruction.
Dwarves: We're to kill any Elves on sight without question. Which is fairly redundant, since any Dwarf would do that anyway. But a paycheck's a paycheck.
It doesn't help that both species are portrayed as being highly xenophobic and Elves believe that all other forms of life (including some of the gods) were failed attempts at replicating their perfection.
In Dominic Deegan, they have the Halflings and the Dwarves going at it, with the pretty Halflings having fruited beers while the ugly Dwarves have more generic beers. That is what's presented at the nature of their conflicts, at least in the modern day.
The Order of the Stick features rather few elves and dwarves long enough for the two to meet- except for the party members. Durkon, a proudly stereotypical dwarf cleric, and Vaarsuvius, The Spock and Insufferable Genius wizard, constantly bicker but respect each others' abilities nonetheless, both being powerful spellcasters. The two did have a little spat when V went round the bend, but the two did apologize to each other later, both admitting that they were in the wrong.
A story arc in Nodwick about ten years back involved a war between the elves and the dwarves over possession of a certain artifact the dwarves claimed had been stolen from them two thousand years ago. It turned out to be a sword which would kill both races if one used it on the other, which forced them to declare a truce.
In Le Donjon de Naheulbeuk (Dungeon of Naheulbeuk)), a French audio Affectionate Parody of tabletop RPGs and particularly Dungeons & Dragons, elves and dwarves famously can't get along. Each race takes its defining characteristics far, far beyond its limits, making the following more or less the norm:
The Elf: (who has fallen down a hole) Help me, I'm stuck! The Dwarf: She says we can leave her behind. The Elf: Get me out of here, it's slimy! The Dwarf: She says she wants us to make rocks fall on her to put her out of her misery.
In Tales of MU, a gnomish folk tale depicts elves and dwarves are the descendants of quarreling twin brothers, who grew into their current forms by attempting to emphasize their imagined differences.
The debate continues even onto YouTube in a segment of D&D PHB PSA. Elves, for those not in the know, cause cancer, and have tiny penises. Especially the women.
Similarly to Naheulbeuk, Reflets d'Acide has elven bard Enoriel and dwarf master Zarakaï constantly arguing.
In The Grim Adventures of Billy & Mandy episode "Here There Be Dwarves!", the plot revolves around a war between tree-dwelling Elves (a parody of the Keebler Elves) and Dwarves over who got what rights to sell food. The Elves, of course, got cookies, while the Dwarves get mushrooms, and have regretted it ever since. In the end, they compromise and make mushroom cookies.
"They taste like my cat!"
There is definitely an undercurrent of this in My Little Pony: Friendship Is Magic, between the unicorns (tend to be educated, higher class and have telekinesis to handle delicate tasks) vs. the earth ponies (strong, hard-working and with a "connection to the Earth"). Among the mane six characters, two of the character foil pairs follow this dynamic, with the dainty Rarity against down-to-Earth Applejack, and the logical Twilight Sparkle against the Cloud Cuckoolander Pinkie Pie.
Athens definitely had a strong military side and they had reasons to consider their military power as famous as that of the Spartans, notably through the largely Athenian victories of Marathon and Salamis in the Persian Wars. The main difference was that in the time after that Athens concentrated on the naval, diplomatic and economic sides of war. But the Athenians' growing military and economic power was what led the Spartans to decide to go to war against them in the Peloponesian War.
The Dano-Norwegian union played the trope straight: Danes were sophisticated, urbanized, even had a university (well-educated to boot). Norwegians were noble savages, free children of nature, and naturally without any sophistication. They could get into the upper classes if they worked hard and played nice, though. On the top of it all, the Danes actually came to admire the Norwegians for this, especially during the eighteenth century.
In modern times, Norwegians are apt to do the trick on themselves: The less urbanized you are, the more "savage" you become. And there is always another country to suck up to.
The North/South divide in the UK between the (now) poorer industrialised North and the richer South. With northerners seen as plain-spoken, down-to-earth and working class (or Northern Bastards) and southerners seen as posh, intelligent, educated, and generally upper or middle class (or Soft Southern Nancies). It is no coincidence that in many fantasy adaptations the Elves have posh, southern English accents, while those for Dwarves tends to be either northern (usually Yorkshire) or Scottish. And then you have the people living in the Midlands who are often counted in both camps...
Anglo/French relations, in a nutshell. The industrial English/British have been at odds with the artistic, sophisticated French for almost a millennium.
On a smaller scale, see Korea (North is Dwarves, South is Elves). South Korea has a high tech industry (with a cyberpunkish Everything Is Online Internet), the national sport is Starcraft, and their army is one of the best equipped in Asia. The Northern economy (that isn't dependent on donations) is based in coal mining, the country is filled with mountains, they pride themselves on strength, and the army is based on numbers. The South Koreans are looking more and more like tall ectomorphic Caucasians, while North Koreans are literally shorter due to the constant famine.
Modern humans and Neanderthals. The modern (anatomically) humans were tall, slender inventive beings with pointy chins and high foreheads. Compare this with the Neanderthals, who were shorter, stockier, with stronger arms and all around more masculine looking, and allegedly master craftsmen. In short, the Neanderthals are dwarves.
Some 19th century pro-Confederate ("Lost Cause") authors depicted the American Civil War as a conflict between a rough, industrial, barely civilized North mainly populated by recent German and Irish immigrants and a gentlemanly, sophisticated agrarian South inhabited by planters of English, Scottish and French extraction.
Which was a bit ironic since in this image the Southern "cavaliers" were portrayed as more sophisticated because their elites were consumers of (mostly British and French) culture while looking down on most of American culture. Also consider where the most prestigious institutes of higher education before 1860 happened to be located and that most of the American writers and poets who achieved prominence in the ante-bellum United States and in the wider world (e. g. Benjamin Franklin, Washington Irving, James Fenimore Cooper, Harriet Beecher Stowe, Nathaniel Hawthorne, Herman Melville) or worked in that era and are still remembered today are from the North. Even Edgar Allan Poe is from a border slave state that did not secede (Maryland), while John C. Calhoun was of Irish stock and Thomas Jefferson and Frederick Douglass were considered embarrassments by the propagandists of the "Lost Cause".
Somewhat reinforced by the Generals who served during the war. Confederate Generals (at least during the first part of the war) made up for the South's material disadvantages by being better strategists. Later on, there are Union Generals Grant and Sherman, who are popularly remembered for their respective ability to sustain huge losses and willingness to engage in scorched-earth tactics.
Actually this can be considered a subversion as it tends to support the image that the Southern elites' main activities were running slave plantations, politics (to further the planters' interests), and the military (the South was then and still is disproportionately represented in the U. S. officer corps). Which really resembles Sparta more than Athens, especially in the South becoming politically more and more monolithic and intransigent before the war.
Although given that mucking about with dual-booting, OS emulation, and/or hackintoshing is inherently more complicated than buying a system off the shelf, it's probably more like Difficult, But Awesome.
This in itself would be a further Elves/Dwarves dynamic: those who buy hardware and software as is, and those that mod/build/tweak to their tastes.