In the original series, Raphael shared some sparks with Mona Lisa, a human girl who got mutated into a lizard girl, but she turned out to be a Girl of the Week.
Michelangelo had a (very short-lived) thing going with a humanoid alien named Kala.
Leonardo got the hots for Lotus Blossom, the lady ninja.
It's implied that Irma had more than a bit of a crush on Donatello. In one episode where Donatello actually stops Shredder's plans in Europe, both April and Irma reward him with a barrage of kisses and hugs.
Donatello has a huge crush on April, but Word of God says it's just for comic relief. However, it is shown that April is actually a mutant, since she is actually a hybrid of Kraang & Human. Also that there is a great support for the pairing by the voice cast & fans of the show.
With the spoiler above, it's safe to say that Casey and April's relationship boarders on this.
Likewise Leo has a thing for Karai. She flirts back, but doesn't even try to hide the fact that she's untrustworthy. However, Karai is soon revealed to be the long lost daughter of Master Splinter & Teng Shen, making her and Leo sort-of siblings. She was kidnapped by Shredder after he had killed her mother.
Futurama, being set in the distant future, has numerous interspecies pairings. Kif and Amy (alien plus human), Leela and Fry (mutant plus human) being the main ones.
Hip-Hip and Hurra: So we have a hippo who has a romance with a giraffe, a weasel who's girlfriend is a kangaroo, an ant who is seen dating a bumblebee, and a crane who has a romance with a caterpillar. Oh, sorry, she turns into a butterfly at the end of one episode. Never mind!
Being a robot doesn't stop Jenny from having romantic feelings for human men.
Brad also had a robotic love interest in a couple of episodes.
Elisa and Goliath of Gargoyles. Complete with plenty of angst about it, especially when a magic spell briefly turns them into the same species.
Demona and Macbeth played a little with the trope before becoming arch-enemies: to quote Greg Weisman, she was “a little bit in love with him” for a while. Macbeth was a good friend to her and the other gargoyles, but he was Happily Married and may have been entirely unaware of her feelings.
Chip 'n Dale Rescue Rangers had the Chip/Gadget/Dale love triangle, them being chipmunks and her being a mouse. Later in the series and comics, it looked like Chip and Gadget were becoming the Official Couple; this was mostly because, in another example of this trope, Dale had become more interested in Foxglove, a bat.
From the same season, "Sea Change" paired the Autobot Seaspray with an alien humanoid woman whose people guarded a magical spring that let any living thing that entered it assume any shape it wanted to.
The Transformers wiki has a list. It comes up more often that it, strictly speaking, should.
Ben 10 has a marriage between a cousin of Ben's and a sludge-like shapeshifting alien, a visit from Grandpa Max's Green-Skinned Space Babe from his days with The Men in Black, and obvious romantic attraction between a mostly humanoid four-armed alien and a floating tentacled brain.
Omniverse also has a princess from the aforementioned four-armed alien race(who just happens to be a great deal more conventionally attractive than the previous one) who has decided she's going to marry Ben. Why? In her species, the superhumanly-strong women marry the strongest man around, i.e., the one able to best her in a fight; Ben kicked her ass when she tried to marry Kevin against his will. There is also the case of Ben and frog-like alien princess Attea who has a thing for him- but only when he's used the Omnitrix to turn into a member of her species, so it may or may not count.
The Nickelodeon cartoon Catscratch has Gordon, a cat, in love with his neighbor, Kimberly. (He calls her "Human Kimberly". Guess what species SHE is.) Making things worse, Kimberly is eight years old and while Gordon's age is never specifically mentioned, he seems to be an adult.
In Alfred J. Kwak, the title character's nemesis, Dolf, is the son of a crow - who, judging from his only apparition in the very first episode, was quite narrow-minded - and a blackbird, an inheritance which is ashamed of, to the point of self-loathing; he even paints his orange beak black.
You'd be hard pressed to find anyone on the Legion Of Superheroes who isn't doing this, since they're all from different planets (e.g. Bouncing Boy from Earth and Triplicate Girl from Cargg). About the only aversion were Lightning Lad's parents, who had about three seconds of screen time in the whole series.
Brian (an anthropomorphic dog) of Family Guy has had a few human girlfriends, and has even had sex with some of them. This is portrayed as perfectly normal in the show's universe. So normal in fact, that Brian acts ashamed when he is attracted to other (non-anthropomorphic) dogs. When Brian actually does have sex with another dog, said dog apparently also had sex with Ted Turner.
Lampshaded at least once. Brian asks a girl out at a party, and she throws her drink in his face exclaiming, "Ew, you're a dog!"
In another episode, his gay cousin Jasper is poised to marry his human partner.
On a side note, Brian had a child with a human woman in a season 6 episode.
Most of any ghost/human romance is between several human girls and the main character who's a ghostly Half-Human Hybrid. (Word of God is that ghosts are a species of their own, rather than all being people who have died, though at least some of them are.)
Jake (a magic talking dog) and Lady Rainicorn (a Korean speaking rainbow unicorn... thing). They're the most successful relationship on the show (which, granted, isn't saying much) and eventually have a litter of rainbow-pupsters. A later episode muddles it further by revealing that Jake is part alien/extradimensional entity too.
Finn, being the Last of His Kind and a Chick Magnet, is surrounded by this trope. He has romantically pursued a candy person, a fire elemental, and (seemingly) a vampire, and has been pursued by, among others, a cloud and a lump of slime.
In the episode "Puhoy", Finn travels through a pillow fort to a land of Pillow People. He meets a Pillow Person named Roselinen and eventually falls in love with her, has two kids and grows old with her before returning to Ooo mere moments after entering the fort.
Ice Kingtries for this, but fortunately is a lot less successful than Finn. Although it's debatable whether or not he's still human anymore.
Tree Trunks (a small elephant) and a pig fell in love with each other. It's adorable.
Invoked in one episode, when Jake demands a romantic story, prompting Finn to order a duck and a fox to kiss.
The next-to-ur example: Clarabelle Cow and Horace Horsecollar in Disney cartoons and comics. Early on, the two are romantic to the point of being engaged (comics, 1932). Later, they're back to being a dating couple, with Clarabelle occasionally seeing Goofy as well ? in one recent comic book story ("With Friends Like These," 2006), clearly doing so to make Horace jealous, though innocent Goofy misreads the situation as platonic and doesn't realize how his friend is using him.
There are also many relationships between ducks and frex geese. Closer than most of the other examples on this page, but still different species.
There are geese within the McDuck family tree as well. Donald's cousin Gladstone Gander for instance is the son of a goose and a duck.
"Treehouse of Horror XIII" spoofs The Island of Doctor Moreau where the characters are turned into animals. After Marge is turned into a puma, she goes to tell Homer about it... and since the lights are off, they both have sex. Homer only realizes the changes seeing how scratched he got. At the end of the episode, Homer gets turned into a Walrus and is shown massaging Marge with his tusk... Yes.
"The Squirt and the Whale" ends with Homer saying a beached whale will get a hot new octopus wife, and that he hears "there's a whalapus on the way!" Marge suggests drawing this. Three guesses what the background images for the credits are.
In "Old Yeller Belly", Santa's Little Helper appears in an ad for Duff beer.
Lisa: Why does a dog have human girlfriends?
Marge: People do crazy things in ads. Like eat at Arby's.
The Backyardigans: Practically all pairings, considered they're all of different species. Bonus points go to any pairing with Uniqua, who we don't even know the species of.
Classic Looney Tunes typically have Pepe Le Pew trying some unintended interspecies romance when he pursues... um, any cat with a white stripe painted on it (Penelope Pussyfoot is the usual victim). (Then, in a sticker book, he shuns a skunk with her stripes painted over!). In rare moments, the roles would get reversed with hilarious results.
Bugs Bunny (when he dresses in drag) and Elmer Fudd (or Yosemite Sam in Hare Trimmed and From Hare to Eternity).
Any time Bugs sings in praise of the "Genie with the light brown hair."
Fifi La Fume (Skunkius sexius, when she came in on a Calamity-Little Beeper story) continues the Pepe Le Pew tradition.
One episode paired Babs Bunny and (human) Montana Max, although they were not quite themselves at the time (Cupid had carelessly let someone take over for him so he could take a day off) and Buster, in trying to keep Babs from walking down the aisle, makes the point that Max isn't her type, not even her species.
Dizzy (his generation's Taz) and his three human girlfriends. An extra level of squick is added when you consider that Dizzy is a kid and the women are... well, women.
In the Minerva Mink segments, animals from many different species and anthropomorphic levels get the hots for her, and in the comics even humans, while Minerva gets the hots for hunky males no matter the species. (One time she fell in love with a werewolf who was only drop-dead handsome once a month, in his werebeast form, but a nerd any other time; she was willing to wait a month.)
In the short West Side Pigeons, Squit (pidgeon) falls in love with Carloota (sparrow).
In the short Wings Take Heart, there's a romance between a male moth and a female butterfly.
In the short Katie Ka-Boo, Katie (human girl) gets a new boyfriend, but it's Chicken Boo disguised.
In Pinky and the Brain, Pinky's recurring Love Interest is Pharfignewton, a horse (which Squicks Brain considerably), in one episode Pinky fell in love with a seal, and he also fell in love with a pig on in the only half-hour Pinky, Elmyra & the Brain episode. It's worth mentioning that the one time Pinky was ever kissed by a female mouse, he ran away screaming.
When Brain creates a clone (known as "Romy") who gets infected with Pinky's DNA, Romy eventually starts dating a human woman, which Brain protests as well.
Brain's recurring love interest, Billie, is also courted by a hamster named Snowball.
In the spin off, Marlene the sea otter briefly holds a relationship with a squirrel due to a pairing mix-up.
The Christmas Special "Merry Madagascar" also has the penguin Private and Santa's reindeer Cupid fall in love with one another.
One episode had Skipper (Penguin) and Kitka (falcon) falling in love.
There's also Kowalski's heartfelt love for Doris the dolphin, and Private's crush on Shawna the zoo nurse in Love Hurts, as well as a ton of Ho Yay coming in from all directions.
There are hints of something more than friendship between Vinnie and Charley in Biker Mice from Mars. One episode also has Greasepit fall in love with Charley for a short time. Another episode has a whole line of women swooning over Modo; while they could arguably be reacting to his suave act, at least one calls him cute. Yet another episode has Modo falling for a bird-woman of some sort.
The second series also has Vinnie finding female cat-women attractive and openly flirting with them.
The 1936 Silly Symphonies short Elmer Elephant is about an elephant whose girlfriend is a tiger.
Likewise, Music Land, released a year earlier, has a saxophone in love with a violin (Interinstrument Romance?). Then, for added Squick, the saxophone's father ends up falling in love with the violin's mother.
The least offensive thing the show did with this trope was get a pig and an elephant to get it on! In the same episode, the offspring of said pig and Mr. Garrison.
"Douche and Turd", where PETA members are shown to be married to animals! And even had a human-ostrich hybrid!
Alvin and the Chipmunks: Whenever the Chipmunks and the Chipettes were not seeing each other, they show interest in humans. In fact, in The Chipmunk Adventure, the Chipettes end up in a harem because a young Egyptian prince fell in love with Brittany and wanted to marry her.
Superjail: Descent into tribal loonydom, constant warfare and, to top it all off, countless male human inmates engaging in reproductive sex with the local canaries. Just some of the crazy shit that happens when the Warden isn't around to run things.
Happens several times (mainly to Jay) in the Men In Blackanimated series. The most serious relationship is between Kay and an alien cop (Kay's feelings for his long lost girlfriend prevent him from going to far).
And for one of the more unexpected examples, Jar Jar Binks has a relationship with the Bardottan Queen Julia. Yes, you read that right, Jar Jar Binks has a girlfriend.
If you think about it, many of the couples in Winx Club could count as this. The girls of the Winx Club are fairies, and the specialists are... human-looking aliens, or fairy and wizard in the case of Layla and Nabu. Near the end of season 4 we learn that Roxy's mother is Morgana, the queen of the fairies. In the last episode of season 4, Morgana reunites with her husband Klaus (a human).
Drawn Together's Spanky Hamm, Captain Hero, and Wooldorf all had a Spin-The-Bottle/threeway make-out session in one episode, another episode had Toot marrying/having sex with Ling Ling's father, Xandir and Toot both kissed (and got turned on by) Ling Ling, a role-play episode implied that Wooldorf molested a human boy, Spanky had sex with a spider (and there were pig-headed spider babies), Spanky and Xandir gay-marry in one episode, another episode revealed Foxy had sex with Wooldorf once...the list goes one, guys, seriously.
And on, and on. Honourable mentions should also go to Captain Hero's (alien) sexual fixation on live-action cow.
Oswald the Lucky Rabbit at first averted this trope by being paired with a female rabbit whenever romance elements in his toons spring up. Then "Rival Romeos" introduced a cat named Ortensia to fill this role, thus playing the trope straight. In Epic Mickey, she and Ozzie has 420 bunny children together.
In the Dudley Do-Right segments of Rocky and Bullwinkle, Nell Fenwick is in love with Dudley's horse, and it's implied that the horse is in love with her as well. Nothing ever seems to come of it, though.
And in the TV series. there was a Pegasus named Heart Throb, a predecessor of Rarity in that she was a hopeless romantic. She also had at least two romances with human men, one of them being Prince Charming, no less!
Spike (a young dragon) has a not-even-remotely secret crush on Rarity (a unicorn). This is also carried over into the universe of My Little Pony Equestria Girls, in which Spike is a dog and Rarity is a human. Rarity doesn't necessarily feel the same way, but she doesn't find it odd either, so it's presumably fairly normal.
Although we haven't seen it yet, pony and donkey relationships must exist because a couple of mules have been seen on the show.
My Little Pony Equestria Girls has Sunset Shimmer (who is actually a pony from Equestria turned human) who used to date Flash Sentry's human counterpart. Twilight also seems interested in him, but it's hardly a romance.
Also, while Irwin's father is human, his mom is a mummy (as in an undead human of Egyptian origins; that kind of mummy). His dad simple claims, "no one can tell you who you'll fall in love with". (Billy tries to ask how it's physically possible, but Irwin's dad purposely dodges the question.)
Actually, Irwin's dad's parentage counts too; while his mother is human, his father is Dracula.
Several dream sequences featured in Arthur that take place in the future has Arthur Read (an aardvark) marrying Francine Frensky (a monkey).
Gumball (a cat) and Penny (a sentient peanut with antlers, revealed in Season 3 to be a shape-shifting fairy) from The Amazing World of Gumball.
Also, Gumball's parents (a female cat and a male rabbit).
There's also Alan (a balloon) and Carmen (a cactus). That can not end well.
And the school's principle, a furry slug, and Miss Simian, a Baboon.
Duck Dodgers of Earth and Queen Tyr'ahnee of Mars were once engaged.
In Slacker Cats Buckley (a cat) wants a romantic relationship with his owner, Louise, but she keeps turning him down. Also he's had sex with good looking squirrels and big rats.
Chanticleer (a rooster) and Goldie (a pheasant) from Rock-A-Doodle.
Johnny Bravo once dated Carol, an antelope he picked up over the Internet. Her ex-boyfriend is a crab.
In Kung Fu Panda Legends Of Awesomeness, it's been shown that romance between different species is acceptable in there. Mantis stated to have dated a caterpillar, a married couple of a male duck and female pig showed up in one episode, and the show hinted at a possible romance between Po (a panda) and Song (a snow leopard).
Betty Boop is good friends with anthropomorphised dog Bimbo, who clearly has a crush on her. Curiously, she started out as a dog too, but soon became a human. Betty was originally made to be Bimbo's girlfriend but she became more popular than him.
The He-Man and the Masters of the Universe (1983) episode "The Return of Granamyr" had the dragon Torm and the human girl Lyra. Torm takes on human form for them to be together. The dragon Granamyr complained that it didn't make any sense, but acted as the priest for the wedding.
Adam (and Adora)'s mom is a female astronaut from Earth that got stranded in Ethernia and then stayed since she fell in love with the humanoid Crown Prince aka Adam's dad.
Creepie from Growing Up Creepie fell in love with Skipper because she believed (like his stage act at the circus) he was part human part spider. She looses most of her feelings for him when she discovers the truth.
Draculaura the vampire and Clawd the werewolf of Monster High.
Johnny Test: Johnny's dog Dukey used to date a sperm whale.
The 2010 Pound Puppies series hints this between one-time characters Cuddles P. Wigglebottom III (a dog) and Madam Pinkiepuss (a cat) in "The Prince and the Pupper", with the hints becoming confirmation in "The Ruff Ruff Bunch". More hints come in "Kennel Kittens Return", concerning Squirt and Fluffy.
In the episode "The Deep End" Mabel has a crush on and shares her first kiss with a merman.
For that matter the first episode, which has her date five gnomes in a Totem Pole Trench. That only half-counts, as she thought that they were human at the time, although she was really hoping he was a vampire.
On Captain N: The Game Master an anthropomorphic octopus falls for Simon Belmont in the episode "l Wish I Was A Wombat Man". The short yet large breasted and curvacious blonde haired pink sea creature took an interest in Simon right away. She wrapped him in her tentacles, gave him a big wink and extended her big red lips in front of his. Simon wasn't interested but the octopus didn't care. Eventually she slithered after him so she could hold and kiss her 'dream boat.' The episode also featured an actual relationship between a talking wombat and a talking cat.
Regular Show: Mordecai (reluctantly) dates Starla in an attempt to get her back with Muscle Man, he also dates CJ, who's a . . . cloud person. Eileen's crush on Rigby could be seen as this, and then Margaret has several human boyfriends early on the show. Turns out she picked that trait from her mom, as the most noticeable example of this trope is her robin mother and human father.
Hello Kitty's Furry Tale Theater has Hello Kitty and friends putting on various plays based on fairy tales and movies. Hello Kitty and Tuxedo Sam the penguin are usually cast as love interests, and likewise Chip the seal and My Melody the bunny.
In the season two finale of Littlest Pet Shop(2012), "The Expo Factor," Sunil (a mongoose) falls in love with Delilah (a cat).
There was also the episode Sweet Pepper, where Pepper (a skunk) falls in love with Captain Cuddles (a weasel).
In the episode Sleeper, Penny Ling (a panda) falls in love with Mr. Von Fuzzlebutt (a raccoon).
In "Secret Cupet" Baa Baa Lou (a goat) falling in love with an unamed female pig.
Russell (a hedgehog) falling in love with Penny Ling (a panda), Vinnie (a gecko) falling in love with Minka (a monkey), and Sunil (a mongoose) falling in love with Pepper (a skunk).
Happens twice in Ewoks. In Blue Harvest, Duloks steal Logray's love potion which in turn causes Fauna, a female Phlog, to court Umwak and then Wicket. In Princess Latara, Latara is assumed to be a real princess, kidnapped and almost forced to marry the sluggish Prince Bork.
Kaijudo: Gabe, a human, falls in love with an Angel Command called Sasha, Channeler of Light; (a Light Creature).
Hot Wheels Battle Force 5: Vert Wheeler & Sage seem to have have a strong bond with each other. This bond is most prevalent in Axis of Evil and throughout Season 2 as he does the best he can to protect her from her twin brother Krytus. One just might call it romantic. However, if they do like one another, it is unknown whether or not either one &/or both of them are oblivious to it, or even if they just don't want anybody to know about it.