Asari are an all female species that reproduces by randomizing part of their DNA using that of any other species regardless of gender as a template. Indeed they're encouraged to do this, and two Asari having a daughter together gets rather looked down upon in their society. Somewhat understandable, in that pureblood couples supposedly increase the chance of Ardat-Yakshi being produced. Liara T'Soni was an Asari romance option for both male and female Shepards from the very first game.
Joker and EDI in the third game. Him being a human and her, an AI controlling a robot body.
Mordin mentions in passing that he's gotten a surprising number of passes from other species... but then he's Mordin so that may not count. He also mentions that Salarians like himself are considered as quite attractive by certain unlikely species.
He talks a lot about interspecies sex. He even gives youThe Talk of the... biological implications of such romance. He notes that chafing will result and recommends you not to *cough* ...ingest.
One time you visit him, he tells you he's currently busy with dealing with an outbreak of a sexually transmitted disease, that is only present in varren. "Implications unpleasant."
After completing a certain quest line on the krogan homeworld EDI will inform you that "We have received several breeding requests for Grunt... and one for Shepard".
A widely popular in-universe film called Fleet and Flotilla is about a turian and quarian pairing. This gets mentioned in Mass Effect 2 by one unlucky-in-love turian. There is also a videogame. The kicker? Legion has played it. And he's terrible at it.
The Citadel DLC for 3 reveals that Tali apparently is a big fan of the musical version of Fleet and Flotilla. It also reveals she borrowed some lines from the movie to give her the courage to admit her feelings for Shepard, in her romance arc in Mass Effect 2.
If Shepard doesn't romance either Garrus or Tali and both survive to Mass Effect 3, they end up together. Both are apparently fans of Fleet and Flotilla, humorously enough.
Turian-quarian romances are a bit of a thing, apparently, as they're biologically compatible, at least in terms of chirality. So there's less of a chance of one or both partners suffering a violent biochemical reaction in case of...ingestion.
Curiously, interspecies couples became significantly more prevalent in background scenes as the series continues, especially in Mass Effect 3, which has seemingly more of them than same-species ones. Such is life during an Alien Invasion — as Joker points out, people have a lot more to worry about than a little public disapproval.
In the Citadel DLC, if you get a female Shepard drunk enough, and she's on good enough terms with him, she and Javik can have a one-nighter. Which they will never speak of again.
BioWare preceded this with the Gay Option in Knights of the Old Republic. Juhani is of a felinoid alien species called the Cathar. It's also heavily implied that she and a female human Padawan were a bit more than just friends.
The Brotherhood of Shadow mod has Arkanian offshoot Koybayasi and Twi'lek Channa Mae/Shadow/Sera Degana. It's a surprisingly sweet note in a very frightening mod.
In Knights of the Old Republic 2, both romance options for a Male Exile are Human Aliens - the Handmaiden is an Echani while Visas is a Miraluka.
Similarly, one of the chapters in The Real Barenziah, a story in Daggerfall, includes the titular Barenziah (a Dunmer) and Therris (a Khajiit) getting together for some lovin'. The books are also in Morrowind and Oblivion, although the version present in both is censored. Barenziah also had an affair with the human Emperor Tiber Septim, and (according to the book) became pregnant by him.
Another book in Morrowind was actually a scholarly tome on the subject of inter-species mating. It stated that all human and Elven species can and do interbreed, with reduced but still possible chances of offspring. Indeed that's how the Breton came to exist. It notes that although there are tales of human or elf having children with the other races, there are no confirmed reports (Oblivion confirms via first-hand evidence that at least Orcs, who are changed elves, can have children with humans (and presumably other elves). As can Cyrodiil-style vampires).
The Last Scabbard of Akrash, like The Real Barenziah, features a consummated Khajiiti-Dunmer romance, although with less detail. The world's backstory also includes a number of alleged Tsaesci ('vampire'-snake-people) - Breton relationships, although the books documenting such are considered propaganda in-game.
The only Romance Sidequest for any male character in Morrowind is a Khajiit woman. She's not picky, of course.
In Skyrim, you can get married to people of any race, except for Bosmer and Khajiit, making this trope easily doable.
Femme Fatale Rouge (a Bat) is officially claimed to have a crush on Knuckles (an Echidna) with additionally flirtatious advances on most of the male cast, Dr. Eggman included.
It's sort of hinted in Sonic Rush that Sonic and Blaze the Cat may have a thing for each other.
In the SatAM continuity, Sonic's girlfriend is half chipmunk, half squirrel. In the comics he seems to have built an Unwanted Harem including other animal characters. In both the cartoon and the Archie Comics, he also competed with Antoine (coyote) for Sally's affections — in the comics, this stopped after Antoine became an Official Couple with Bunnie Rabbot (Cyborg rabbit), who first showed a brief hint of having a thing for the cowardly pseudo-French coyote in one episode of the cartoon. And in both canons, Bunnie's attitude towards Sonic, particularly before hooking up with Antoine, could be taken as flirtatious, what with her frequent reference to him as "sugah hog".
Tails (fox, albeit a slightly mutated one) and Cosmo (Seedrian - a species evolved from plants) in Sonic X.
Agarest Senki has five different human/non-human matchups across the four generations, and the fifth generation can choose one of the girls not chosen in a past generation. As said romances consist of a Syrium (an elf-like race), a neocollom (kitsune) with god's blood on her mother's side of the family, two elven hybrid sisters (half High Elf, half Dark Elf), and a Featherfolk (angel-like Winged Humanoid), this isn't as improbable as it may sound. There's also teasings of a homosexual version; the hermaphroditic god Deeth flirts with Dyshana in female form and gets hit on by Thoma after she mentions she should have shown up in male form. Both Dyshana and Thoma are human.
Star Fox 64 has Katt, who seems to have a thing for Falco (can you guess their race?).
Pretty much any Dungeons & Dragons-based game (see below) that has any sort of romantic capability will have Interspecies Romance. It's almost blasé in D&D, though some settings make a point of having a xenophobic nation or two - almost always evil or at least repressive to take the moral of the concept from plain obvious to Anvilicious.
For a more old-school reference, there is a sex scene between the Captain and Talana in Star Control 2. It is almost a But Thou Must although if you refuse enough you can skip it.
There is also Admiral ZEX, who there is not a (canon, at least) sex scene with, despite the fact that he has a very clear interest in the Captain. This is partly because of the fact that he's male and partly because, unlike Talana, he looks nothing like a human.
Breath of Fire I features the neighboring villages of Tantar and Tuntar, one of which is populated entirely by humans and the other is populated entirely by the "forest clan," people who look like this◊. The two villages get along incredibly well, and in fact, when the player first arrives, both are celebrating the fact that the first forest clan/human marriage is about to take place. And it does, though you have to do a bit of a Fetch Quest to save both villages from an imminent threat before the actual wedding. (Forest clan male/human female, if anyone was curious.)
A cutscene in Breath of Fire II retroactively reveals that Ryu (dragon clan) and Nina (bird clan) from Breath of Fire I got together, and the current bird clan as of Breath of Fire II is weaker due to being less pure-blooded due to being descended from that pairing. That's why the bird clan in Breath of Fire II can't shapeshift without a special irreversible ritual, whereas they could go back and forth at will in Breath of Fire I. Much less extreme than the first example, since the clans in question are both basically human with some magical traits added.
The Bird Clan seems to love the species so much, that, by the time of Breath of Fire III, the entire clan have essentially lost their wings, becoming boring old humans. Making the hero and heroine of every Breath of Fire game Ryu of the Dragon Clan and Nina of the Bird Clan doesn't help matters either.
Also in Breath of Fire II, both that generation's Nina (a winged human), and Katt (a half-furry catgirl) develop crushes for Ryu. Ryu's friend Bow (an anthropomorphic bulldog) has a thing for Nina's sister Mina (also a winged human). Sten (a monkey man) tries to blackmail Nina (and later Katt) into a date. And hell, even Ryu's own parents are an interspecies couple (a human and a dragon).
Rand's mother Daisy in Breath of Fire II is of...somewhat debatable race, looking more or less like a human, though slightly larger. Whatever she is, though, she looks absolutely nothing like her very obviously armadillo son, which raises certain questions about his unseen father. Although, to be fair, the female representatives of some races (including Rand's race) tend to look much more human than the males.
Breath of Fire III teases Slap-Slap-Kiss-style Unresolved Sexual Tension between Momo (technically a dog, though the degree of anthropomorphism is so far toward human and the ears look so much more rabbit-like than dog-like that she more like a bunny-girl than anything else) and Rei (weretiger) from time to time.
Bleu/Deis, a somewhat perverted lamia-like snakewoman, who hits on the different Ryus throughout the entire series.
In the second Spyro the Dragon game, Spyro and Elora (a faun) seem to have a thing going. Hunter the Cheetah also pairs up with Bianca the bunny in the third. Then you've got Romeo the Land Blubber and Juliet the bird... the games have a lot of these.
Final Fantasy IV, Cecil and Golbez were sired by Kluya, a Lunarian (that is, an alien from a very, very distant world, who eventually settled on a moon orbiting the game's planet,) from a human mother. Cecil goes on to have children of his own, again with a human mother.
Final Fantasy VII, Aerith, the last Cetra, is the daughter of a human scientist named Gast, and a Cetra woman named Ifalna. Of course, the Ancients are almost entirely human themselves, so there's really not much of an issue here, until Hojo comes along and tries to mate Aerith with Red XIII, a huge talking wolf/lion that is another Last of His Kind. There's no indication that Hojo's idea would have actually worked, though. According to the Compilation, there was at least one more, female, member of Red XIII's race, who had been his mate before he was captured by Shinra.
In Final Fantasy IX, Garnet and Eiko were Summoners, apparently a different species from normal people, since they were born with horns. Also, Zidane's not entirely human either — obvious from the start since he has a tail, but this turns out to be more than a cosmetic quirk. And then there was the Vivi/Quina marriage, which involved a techno-magical construct and an ambiguously gendered giant frog thing.
In Final Fantasy Legend, not only does this occur, but it's so common that nobody bats an eyelash about King Armor (human, or close to it) falling in love with a girl that uses the same sprite as beholders and slimes!
Final Fantasy XI, being an MMO with five humanoid races and all, is bound to have plenty of romance, found both in the player base and story lore. The tragic romance between Raogrimm, a Galka, and Cornelia, a Hume, became the catalyst of war. The main character of Wings of the Goddess, Lilisette, is apparently the offspring of an Elvaan and a Hume, in a game where cross-breeds were never mentioned before. Also, one cannot deny the massive amounts of Tarutaru x Mithra doujin...
Final Fantasy XII has a little shipteasing between Fran and Balthier, particularly in the Pharos after defeating Dr Cid. Revenant Wings expands on this - when Tomaj attempts to romance Fran, she tells him Balthier's methods were different.
Also, there is a sidequest in Rabanastre in which you can pair a Viera up with a Hume. The Hume tells the party that he wouldn't have imagined a Viera/Hume pairing could work until he saw Balthier and Fran.
Blazing Sword, Ninian the half-ice dragon is a possible mate for the human hero Eliwood. Nergal (human) and Aenir (ice dragon), the couple that spawned Ninian and her brother Nils.
Interspecies Romance between Beorcs (Humans by Any Other Name) and Laguz (humans who can shapeshift into animals) is all over the place in Path of Radiance and Radiant Dawn. In fact, some of these romances are either directly or indirectly responsible for most, if not all of the events in the two games. Though in this its somewhat Justified as Beorc and Laguz share a common ancestry.
In Fire Emblem Awakening, Nowi and Panne are potential wives for the majority of the male characters, and are of the Manakete and Taguel races, respectively. The aforementioned Tiki also makes an appearance as a young adult, but will only be able to marry the Player Character.
From the second generation, shall Nowi and Panne be married, we'll meet Nowi's haf-Manakete daughter Nah and Panne's half-Taguel son Yarne. They can also marry their human companions, or the Player Character.
Also possible between humans and Sepps (see Endorph ending). Might happen between Revya and Danette in the future after the Danette (male) ending. See Victorious Childhood Friend.
Sepp/human pairings may actually be quite common. One NPC in the game claims to be half human half sepp, Levin (sepp) has a crush on Tricia and may also hook up with Revya (if female) in the Levin-ending. Female Revya can also hook up with Gig, the God of Death in one ending.
The Warcraft series has a few of these, as early as Warcraft 1: Orcs and Humans there was Garona the Half-orc and Griselda and Turok, a female orc and male ogre respectively; Warcraft 3 reveals this coupling produced Mok'nathal (ogre-orc). Less extreme examples have been the inevitable human male/Female elf pairing as with Alleria Windrunner and Turalyon (human), as well as Veressa Windrunner and Rhonin (same combo). There's at least two orc/draenei couples, and one character, Med'an, who's the child of one of those last and Medvih, thus making him 1/4orc 1/4draenei 1/2 human, though you wouldn't know it if you saw him. It's also hinted that Kael'Thas (yet another high elf) had a crush on Jaina Proudmoore (human), and furthermore, many people speculate that Jaina has a romantic relationship with Thrall (orc).
World of Warcraft has Marvin and Tamara Wobblesprocket, who are a married couple. The former is a tiny gnome, and the latter is a human.
Archaeologist Adamant Ironheart (Dwarf) and Priestess Kyleen Il'dinare (Night Elf) seem to have something going on, too. At least, she doesn't mind him calling her "darling".
The Troll Zebu'tan is forever trying to woo the Blood Elf Alys Vol'tyr. She isn't very receptive to his advances, but her dialogue makes it pretty clear that it has little to do with his species; she doesn't want him because she's spoken for and he's a creep.
World of Warcraft has several "Steamy Romance Novels" that can be pickpocketed from NPC humanoids. One of these describes a romance between a male human paladin and a female undead rogue. Another one of them describes a romance between the same paladin and a female gnome warlock. There's also Anveena (human embodiment of the Sunwell) and Kalecgos (a blue dragon). Possibly also Tyrygosa and Jorad Mace.
Ever play the classic arcade game Joust? When you destroy one of the vulture riders, the vulture lays an egg that you must collect to complete the round. If it is allowed to hatch, an enemy human emerges, and a new flying steed comes in to pick him up. The question is, why does this happen? An explanation comes to mind...
Tales of Rebirth has a gajuma(beastmen) princess loves a huma(human) general seems one-sided until she dies at the end and he realizes that he loves her too, giving it a Bittersweet Ending.
Tales of Symphonia gives us several pairings between humans and elves. Pairings between angels and humans do not count because angels were just humans and half-elves with their bodies modified to resemble that of what people believed angels to look like.
Tales of Symphonia: Dawn of the New World gives us not one but two canon inter-species pairings: Marta/Emil and Aqua/Richter, though the former eventually can live out their lives as humans and the latter is one sided.
In The Sims you can sleep with robots, zombies, vampires, plant-creatures, aliens, werewolves, etc.
Mega Man Zero 4 introduced two characters, Neige (human) and Craft (Reploid). The latter even explicitly stated that he fell in love with her, and their romance is a very important turning point in the game!
Earthworm Jim, whose name speaks for itself, has a huge crush on Princess What's-Her-Name, who is a humanoid insect. On the other hand, if they're really all cows then this trope is averted.
Ar tonelico: a part-RPG, part-dating sim whose dating sim aspects revolve entirely around relationships between humans and Reyvateils - an all-female race of magical girls whose ancestors were artificial intelligences created from scratch using alchemy. You can also date said at least one of said ancestors, who's immortal and still around.
The Legend of Zelda: The Wind Waker, a girl named Maggie asks you to deliver a love-letter to her love at the Forsaken Fortress. As it turns out, the person she met and fell in love with while being held captive there is actually a Moblin — one who is torn between wanting to return the affection and wanting to eat her. In addition, Link gets hit on by the Queen of Fairies. He appears to actually quite like it, much to the King of Red Lions' annoyance.
The The Legend of Zelda Oracle games have a good dose of this, too. In Seasons, Link (Hylian) dates the Subrosian pop star Rosa (and, in the manga, draws the romantic attention of his pet chicken, Piyoko). In Ages, Link gets propositioned by the Maku Tree, and Queen Ambi pines for...the undead Piratian Captain. Then again, since he's been stuck in another world for years, he may have been human a long time ago.
Crow, the heroine's bird companion from The Longest Journey, claims he's made advances to female birds of multiple species, although it's not clear if his efforts were successful or if he's just making it up.
Pokémon, mentioned in the anime section, gets another mention due to the prevalence of Hot Skitty-on-Wailord Action, which appears more readily in the games than the anime. However, it is said that all Pokemon are descended from Mew, which would make them technically all one species.
According to Sinnoh legend in the English version of Diamond/Pearl/Platinum, at one point, humans and Pokémon "ate together at one table". This is a Bowdlerization of the original Japanese line that explicitly states marriage occurred between the two. One of the egg groups is called "Humanshape"...
Pulseman tells of the titular character being the offspring of a man and an AI. Yes, man and machine had a baby. By combining his DNA and her program core, when he digitised himself inside her.
Most of Ratchet's Girls of the Week in the Ratchet & Clank series qualify. For a slightly more brain-damaging version, there's an amnesiac Captain Qwark apparently once hooking up with a monkey. (This revelation is, naturally, treated as Too Much Information).
In Ōkami, the Ship Tease between Ammy and Issun kicks to high gear minutes prior to entering the Final Dungeon, with some very suggestive lines from Issun. Keep in mind, Issun is a wood sprite roughly the size of a person's hand and Ammy is the sun goddess in wolf form.
There's also the matter of how her son Chibiterasu from Ōkamiden came to be, despite that it's implied the only ones left alive on the celestial plains are the celestials (Something close to humanoid angels) and Wakka.
In Mana Khemia one of the human (sort of) protagonist's possible love interests is a catfolk named Nikki, and if you manage to get her ending, not only do they get married, but they also have kids.
Pretty much all of the girls in Thousand Year Door seem to like Mario. All four of his female party members (a Goomba, a talking cloud, a shadow siren, and a mouse) give him a kiss on his cheek at one point. Vivian even comes close to telling him her true feelings for him at the end, but then decides that he'd be much better with Peach.
"We've got to help, Delphi. Yes, she may be different to us - slightly taller and a different colour - but I love her, you hear me, I love this woman!"
Rogue Galaxy have Deego (big bulldog person) and Angela (the not-quite-elf).
Gish has a titular protagonist rescuing his human girlfriend. And in a good ending they have even get married. In the mobile phone port, they even have children.
In Dragon Age: Origins, none of the party members you can pursue a romance with (consisting of three humans and a male elf) care what race the player character is, be he or she a human, elf, or dwarf. However, if a dwarf, the romantic interlude is as awkward as one might expect.
Dragon Age II has an always-human player character and two elf love interests, neither of whom particularly mind despite the setting's use of Enslaved Elves. Of course as a hunted former slave himself, Fenris has bigger things to worry about than social taboos, while Merrill seems to decide that the Dalish disapprove of her choices anyway, so what's one more broken rule?
Isabela admits to having slept with humans, elves and a "dwarf in drag once", but doesn't recommend the last one. She has a history with Zevran established in the first game and becomes Friends with Benefits with Fenris if neither of them are romanced.
While no romance occurs, Merrill once admitted to finding the Qunari particularly "easy onthe eye". She may or may not be aware of Carver's crush on her.
Dragon Age: Inquisition brings back the ability to choose the Player Character's race, resulting in all the same race combinations as the first game, with Qunari added to the mix.
BioWare did it again in Neverwinter Nights: Hordes of the Underdark, where your character can romance all but one of your companions in Acts II and III (a female drow, a male tiefling, and a female elf ghost), as well as an NPCtrumpet archon.
Guaranteed for female player characters in Neverwinter Nights 2: Mask of the Betrayer, where the romance option is Gann, a hagspawn. Gannayev is the product of an interspecies romance (night hag/human) as a romance option for female PCs. He has no objections based on species either. Neither does Safiya, a human, if the male character is a non-human.
In Brutal Legend, this is how Eddie came to be. Demon Emperor Succoria and her human slave-turned-assassin-turned-lover settled down in the future after Succoria realized that demons would lose control of the world and humans would come to rule the Brutal Land, and she had a Villainous BSOD.
In the art book for Phantasy Star IV, there's a bit of information about what happened to the heroes after the events of the game; Chaz apparently dies of illness sometime before he's thirty, leaving Rika, who has since become a guild hunter, to care for their young son, Rui, by herself.
In one of the Harvest Moon games, Animal Parade, either gender of player character can choose a god or mage as their Love Interest. In the latter case, the Witch and Wizard don't seem particularly nonhuman, but there is at least one moment where the Witch makes a point of referring to the main character as a human.
A better example is the Harvest Goddess and Harvest Lord in Animal Parade. A Harvest Goddess is available for marriage in Mineral Town, DS, and Hero of Leaf Valley. Before Animal Parade, what did female players get? A Kappa.
Harvest Moon DS even added a mermaid for you to marry. Yes, a mermaid.
In Rune Factory 3, the main character's parents (although you never actually see them) were a human and a wooly (sheep-like monster). Two of your possible love interests are Kuruna (an univir, a magical horned humanoid) and Pia (a mermaid). Another girl, Raven, is half-human, half-phoenix. Plus there's Gaia's (who is a dwarf) crush on Evelyn (a human).
There's also Rune Factory Frontier, where two of your love interests are Tabatha, an elf, and Iris, a vampire (it would seem vampires in this universe are a separate species, rather than being undead).
A strange example is found in Magna Carta 2, where Celestine falls in love with Argo at first sight. Everyone but Celestine finds it all... Awkward since Argo's a massive creature who looks like a mix between a Dragon and a Hawk. He does eventually warm up to her however.
Strange Journey makes fun of this: whenever Anthony falls in love with a demon, he asks you to go, find the demon and send a message of his love...and every time he tells you he's in love with a demon, the music comes to a dead stop. And every single time, he's put down by the other party in the most humiliating fashion possible, though much of that is his own damn fault (spoiler warning, Anthony: if a demon looks like a little girl, it probably thinks like one, too). Except for Skogsra, who's genuinely thankful she got an apology for his cowardice, and Gemori, who gives him some romantic advice per her job as a god of love.
The dog-people Caninu and cat-people Felineko of Solatorobo are quite capable of having children together. Both ships that are teased to any great length are interspecies.
Radiant Historia has a side quest called "Mankind and Beastkind" in which you show a Satyros woman named Liese that the love she shares with a human gatekeeper shouldn't be hindered by the fact that they come from two different species.
Your Satyros party member, Aht, has a major crush on the (human) main character, Stocke. He doesn't exactly reciprocate the same feelings, however; not because she's of a different species, but because she's 9.
In Kamidori Alchemy Meister one of the three main love interests is an elf. The main character is also known for getting along with all kinds of supernatural creatures, including elementals, angels, kitsune, succubus and more.
In I Miss the Sunrise, your options of crewmates to pursue romantically are not limited to species. You are free to play a human character who professes their love to Lizard Folk, or vice versa.
Startopia has the sirens (winged humanoids) providing (PG friendly) 'love' to a variety of species, from little grey aliens to giant aristocratic slugs.
Most Touhou shipping ends up here since the majority of the characters are various types of youkai. Canonly, Rinnosuke Morichika is the result of a human/youkai pairing, and Keine is half hakutaku (a lion-dog with horns).
League of Legends: human Jarvan and half-dragon Shyvana are...close, put it that way, and Blitzcrank's dating service ships Rammus the armadillo with a cactus (whether it's the one from Plants vs. Zombies remains to be seen).
Relationships between other especies are implied, but rarely explored. In one particular sidequest, a female Homs shows interest in several men, one of them a Nopon, but her interest in him quickly goes away once she realizes just what she's doing.
It's a bit of a spoiler for this example to be here, but here goes: Catherine can potentially end with this trope, with the human protagonist Vincent and the succubus Catherine hooking up.
Octodad has the eponymous male octopus and his human wife. Their two kids are also human. When his wife and son (his daughter already knew) finally find out that he's an octopus, they happily accept him. Though his son does ask how he and his sister were born...