In real life, gem appraising, cutting, polishing, faceting, etc. is a multibillion dollar industry. Not so in fiction. Not only are they much bigger, they're just naturally flawlessly cut and perfectly shiny, even while they're still in the ground, or where there's no logical way they could have been cut. Characters will find these gems studding the walls of a mine, lying close to the surface, or lying casually in open fields. Bonus points if there's also clumps of different types of gem. Any place where they're abundant is usually a City of Gold.
While tumbled pebble gems may look "polished," and really good mineral samples can have well-formed crystals, most of the ones commonly considered very valuable (diamonds, emeralds, sapphires and rubies) do require quite a bit of work to be presentable. In the rough, they look like all other dirty, randomly shaped rocks, so much as to be passed over as such by the untrained eye. The common gem shapes seen in jewelry stores aren't naturally present in any gem. The circular diamond with a pointed bottom, rectangular emerald, and perfectly rounded opal were designed that way to best showcase the gem (for instance, the "brilliant" cut for diamonds maximizes their sparkle by angling reflected light back through the top of the stone).
This is probably an Omnipresent Trope. Subtrope to Artistic License - Geology. Related to the Rule of Perception (as many viewers would be unable to identify uncut gems as such without being explicitly told what they are) and Color-Coded Stones (when stones are only distinguishable from each other by explicit colors)and could lead to Reality Is Unrealistic. Not related to All-Natural Snake Oil.
Superman in the Silver Age and Bronze Age was known for squeezing lumps of coal into diamonds. Aside from being bad science for other reasons, the diamond produced was always a cut diamond with facets.
Jurassic Park has someone pull amber out of a mine, and it is shiny already. All the miners did was grind off some of the rock in which the amber was encased.
In Snow White and the Seven Dwarfs, the dwarfs' mine has a huge variety of gems that are all already perfectly cut. Doc's evaluations aren't even really about their carats, but whether they "sound" good via tapping them.
In Congo, the diamonds in the ancient mine are already sufficiently well cut that one can be plugged straight into a commercial laser for huge power boost.
This occurs in Lloyd Alexander's Chronicles of Prydain novel The High King. While going through a Fair Folk mine tunnel, Glew finds a large number of uncut gems that are sparkling, glinting and glittering. (Homage is paid to the trope though: Doli comments that those stones are really worthless, and even the work of a jeweler wouldn't improve them much.)
In Andre Norton's Storm over Warlock, Shan and Thorvald find green crystals embedded in the cave as they flee through it. However, though the stones might have been worth a fortune, they hurry on, since they are fleeing for their lives.
In Andre Norton's The Zero Stone, the Guild ship's landing brings up crystals that Jern can see at a glance, though he can't tell their worth.
In an episode of Saturday Night Live hosted by Christopher Reeve, there was a sketch showing how Reeve got the Superman part. He screws up the "turning coal into diamonds" bit by using too much pressure, but gets the part anyway.
In an episode of The Adventures of Superman, Superman made a new diamond to replace a diamond in a native statue in the jungles of the Amazon.
In Smallville, Clark squeezes a lump of coal into a cut diamond and uses his heat vision to set it in a ring for Lana. Of course, that whole episode ended up not happening.
With the addition of mining for ores, The Elder Scrolls V: Skyrim allows the player to also occasionally find precious gems. Most of the time this trope is averted, with the gems being rough and flawed, but occasionally, the Dovakhiin can dig up a perfectly flawless, pre-cut gemstone. Out of an iron vein.
The more primitive mining system from The Elder Scrolls III: Morrowind featured diamond veins that looked like elongated, beautiful bluish-white crystals poking out of a boulder. You can take cut diamonds from it.
In Mega Man 9, Jewel Man's stage has enormous pre-cut gems inside the ground.
To be perfectly fair, gem quality diamonds really do take on an octahedral shape in nature that looks a bit like Jazz Jackrabbit's diamonds. However they're very rarely as perfect as those diamonds.
In Minecraft, while some materials, such as iron and gold, have to be mined as unrefined blocks and then smelted into usable forms, diamonds pop out of the wall as the aforementioned symmetrical, visibly faceted lumps.
Any jewel or precious stone mined in the Harvest Moon and Rune Factory series. Curiously, precious metals do not come already in bar form.
Its three other existing mines also sometimes have stones of eXtreme power or lumps of (cut) diamond in them, but considering they include ores like cardboard, linoleum or velcro, expecting gems to be cut is the natural thing to do.
In Spelunky, gems mined from rocks are as much polished as ones found in treasure chests or on ground.
The pleasant corollary is that these gem deposits are absolutely everywhere, and are considered almost valueless (Rarity uses them to decorate stage costumes) if sparkly. Finding an exceptionally large gem (like the Fire Ruby Spike is shown saving for his birthday dinner) or a set of perfectly-matched gems may be difficult, but finding gems is quite easy if you know how to look.
On The Simpsons, the mine run by a crazy woman using enslaved apes in Africa has gems like this.
In an episode of Ducktales, Scrooge buys a coal mine, and his nephews question why. Scrooge answers by tapping a particularly large chunk of coal (which was just lying around for some reason), and it collapses, revealing it was just a black crust surrounding a perfectly cut diamond, so large Scrooge can lean on it.
No really, crystals naturally do form gorgeous flat shiny facets in nature, just look at the inside of any geode. In fact for most of the human history involving diamonds, cutting or polishing a diamond was considered a sacrilege, a foolish boast by a human being who thought he could polish as well and perfectly as nature did.
When Lina is going through her loot after raiding a bandit hideout in the first season of Slayers, she notes that a large number of the gems are flawed and not worth much. She then enchants them into protection amulets so that she can sell them for more.
Phule's Company had a Lampshaded aversion. Phule's dialogue with the local gemstone magnate goes like this:
Charlie: In fact, I've got 'em with me if you'd like to see. (shows a handful of pebbles) Phule: Uh... Very nice. Charlie: (shows his ring) ...This is what they end up lookin' like. Phule: (really meaning it this time) Very nice.
In The Phantom Tollbooth the Numbers Mine is of the ordinary sort. Carts of rough stone are being pushed around, and men are explicitly sitting at buffing wheels on site. The Mathemagician has to reach into their carts to get polished stones. The weird thing is; the residents of Digitopolis consider diamonds, emeralds, etc. to be worthless, yet they still polish and cut them before tossing them out.
In the second Artemis Fowl, Mulch Diggums uses dwarfish rock polish to melt a window to break into a home; he pauses in his internal monologue to mock humans as he does so, for cutting gems to make them presentable, which he considers to be a waste of gemstone.
A good portion of Airman takes place at a prison where the prisoners mine diamonds. At one point, a guard frustrated at being unable to stop a supposed boogeyman starts chucking uncut diamonds into the sea, thinking they're just rocks. A smarter guard notices them for what they are, and realizes the "boogeyman" is actually part of a heist.
In Twenty One Balloons, the diamond mine of Krakatoa is explicitly stated to have the diamonds as lumpy rocks. The founder of the island has to shatter one of them into planes to form an axe blade.
In King Solomon's Mines the cache of diamonds is composed of uncut and rough-cut stones, the largest of which are badly flawed and/or off-colour.
In the New Tricks episode 'Diamond Geezers', the reason that the diamond at the centre of the episode has lain undiscovered in a flat in East London for decades relates to the fact that the flat's owner, a jewelsmith, was too nervous to cut it; it looks just like a large red gem and most people treat it as such (though a jeweler's assistant does identify it as a diamond after a quick look.) Does kind of count as Treasure Is Bigger in Fiction, though, as it's about walnut sized and red.
In the Elementary episode "The Leviathan", Holmes notices that some of the stones are missing from a coffee-table decoration comprising glass tubes of different-coloured gravel, and deduces that this is where the uncut gems were hidden.
RuneScape - mined gems are uncut. In order to use them in jewelery, the Crafting skill is required to cut them first. It also gets into the realistic zone in that the gems don't just lie on the ground but have to be mined - and in that certain gems are found with certain ores.
The dwarves in Dwarf Fortress mine out rough gems that need to be cut before they're usable. The later versions even have different kinds of cuts, depending on the type of gem.
The Sims 3 includes rough gems (and unrefined ore) scattered around the town that sims can pick up and send away to be cut into numerous different designs. Some gems have special properties that can't be used until after they've been cut.
In Harvest Moon: Animal Parade, you find uncut "Wonderfuls" of various colors in the mine. They're next to worthless unless you have Mira cut and refine them, and she has a good chance of failing, too, meaning you'll want to mine a lot if you want to find all the good gems.
Diablo II's socketed items can be fitted with gems of many grades, the lowest being Chipped and the highest being Perfect. The game also has the refining process present in the Horadric Cube.
World of Warcraft has an entire Jewelcrafting profession available, in which the player takes raw gemstones and grinds and polishes them into something usable in Socketed Equipment. Jewelcrafting also gives the prospecting skill that allows a player to sacrifice raw metal ore for random gems (that are sometimes more useful and sometimes less useful for Item Crafting compared to the ore).
In the flash game Ravenwood Fair, gems fresh from the mine are uncut and lumpy. A machine to cut and polish them must be obtained by completing challenges.
In Arcanum, not only all the gems are either found in chests or obviously dropped on the floor by somebody, but there are rough jewels, which look like misshapen shards of coloured glass and, of course, cost less.
In A Tale In The Desert, not only do you have to carefully cut gems yourself, plane by plane, you have to take advantage of inherent flaws to get any concave aspects.
RF Online allows the player to obtain various gems through processing unrefined ore, with different tiers of ore resulting in different qualities of gem. However, a player can literally go through hundreds of ores before receiving any gems (however given that a player can haul in a few thousand at a time, this is usually not an issue).
Gemstones that form inside what are called Pegmatites really do this. The nature of a Pegmatite is a pocket where lava flowed up towards the surface, but then subsided before actually reaching the surface, leaving a holly typically chock full of rare elements from the lava. The elements then grow into crystals, which, since they are inside a hollow, have nothing to impede their formation and take on large naturally faceted shapes. Quartz in many varieties, Topaz, and Tourmaline all form inside pegmatites this way. Geodes are essentially really tiny pegmatites while large ones are worth hundreds of thousands of dollars.
Diamonds will naturally take on one of three shapes, an octohedron, a cube or rarely a dodecahedron. Octohedrons are often well-formed and clear, and good specimens that naturally facet themselves are called glassies and highly sought by collectors.
Garnets naturally form ploshed dodecahedrons, but as garnets aren't super-hard and form under great pressure, the edges tend to get worn.
Rubies and Sapphires have a natural triangular structure, but due to cyclic twinning rubies typically form nice faceted hexagonal prisms, while sapphires take the shape of long spindled double-pyramids with six sides.
Though too soft for most jewelry purposes, Fluorite is dearly loved by collectors because it naturally forms extremely exact cubes often combining many colors into one specimen.
Calcite has more possible crystal habits than almost any other gem and can come in all sorts of natural gem-polish shapes.
Ultimately almost every single gemstone aside from a few aggregate types like Malachite, Opal, and Jade can do this. If the gem comes in crystal clear (aggregates are usually translucent to opaque), odds are it will form All-Natural Gem Polish at least once in a while. Specimens that do so in particularly good formations are usually too valuable to cut and are kept in their natural state by collectors.