The whole point of the Monster Girl Encyclopedia from Japan.
In The Gamer's Alliance, Omaroch and Delora are a demon and a human who fall in love although such union is seen by many as blasphemy. The Land of the Living witnesses several intermarriages between different races, including elves, humans and dwarves among others, which result in children with mixed ancestry such as half-elves. Interspecies romance becomes a major plot point with nymphs who need males from other races to breed because a magical curse makes them only give birth to female nymphs; this causes them to have no males of their own to keep their population going so they need to seduce men from other races in order to become pregnant and stop the nymph race from becoming extinct.
Carmilla and all her more-or-less human entourage, in the Whateley Universe. In fact, with a major-league lust demon for a father and a human/Deep One hybrid mother, Carmilla is also the result of one of those...and from what we've seen of her dad since he showed up in the stories, which basically paint him as a devilishly charming rake with some trouble keeping his tentacles to himself who honestly dotes on his only daughter, romance may well have actually figured into it.
Aside from the above, we've also seen hints at possible romance between one or two of the students and members of the local tribe of lycanthropes, and of course there are plenty of mutants whose mutations have forced them into more or less inhuman forms with little hope of reprieve. (The technical term is GSD, for 'gross structural dystrophy' - 'gross' in the sense of 'overall', mind you.) While the latter may still be technically and legally human, speculations about their potential present or future love-life (such as the Fury Twins idly musing on their chances of finding a boyfriend) necessarily do invoke this trope.
Egg and Kube's relationship probably qualifies, though it's not quite as obviously romantic as the above.
While it's unconfirmed and seemingly one-sided Kaja and Crez also come under this trope - Kaja is a bizarre Angel and Crez is... Crez.
The art of Fredrik K. T. Andersson does this a lot, with plenty of hybrids, half-human or otherwise, resulting. The Bard is the most infamous, having bred with a dragon, a werewolf, a minotaur, a naga, a scorpion woman, a centaur, a rock and possibly some more. The rock case is lampshaded. Here are six of his girlfriends with children (NSFW for scorpion breasts).
Neopets, full stop. It seems that any species of Neopet can breed with any other, leading to what can best be described as 'unusual' family combinations...To the point where a simple family of four could all be different species.
The Nostalgia Chick talked about how this was a bad idea in her "Science going wrong" video. "Don't put your dick in it!"
But she also says “beauty soothes the savage beast,” if you’re female, you should let the creature put its dick in you.
In Disney World of War there are several and the most prominant are Scatani, Scamp (dog) and Vitani (lioness) and Berlielle, Berlioz (cat) and Danielle (dog).
Someone keeping track from Elcenia's Rhysel's point of view would assume this was the norm on Elcenia. Though it isn't entirely, it is assumed that a dragon will go through a number of non-dragon mates before settling down with a dragon—dragons live a long time.
The Journal Entries are practically MADE of this trope. There are VERY few ongoing relationships in which all people are the same species.
Has happened sometimes in We Are All Pokémon Trainers. At some point there are romances between humans and Legendaries, such as Luke with Reshiram and Jane with Zekrom. (Both ended up breaking up though.) In a later case, Sierra's boyfriend Vyvyan is baleful polymorph'd into a Rayquaza.
Foul Bachelorette Frog is a red-eyed tree frog, and Foul Bachelor Frog is an American bullfrog. Two very different kinds of frogs that don't even live in the same part of the world, and so would never even see each other, much less mate. But the two memes have been combined into "Foul Frog Couple."
Enoriel is revealed in later episodes of Reflets d'Acide to have had a romance with Alia-Aenor, though she was posing in a human form when they met. As soon as he learnt what species she really was, he ran away out of fear.
Subverted in The Jenkinsverse, where humanity is the only species to have any members who aren't squicked out by the idea. Sadly for those few, even if they did find an alien who was open-minded enough to try, humans are so much stronger by comparison that any such union would inevitably end in serious injury or death.
LINE, a family of Japanese social networking/gaming apps, has Cony (a female white rabbit) dating Brown (a creatively-namedmale brown bear). Brown's ex-girlfriend is Sally (a baby chick); and Jessica, a cat, has James (ostensibly human) and Moon (indeterminate species) as potential love interests.
In the Dr. Doug episode of With Special Guest Lauren Lapkus, Tawny (played by Lauren Lapkus) and her dog have what turns out to be a realistic and complex relationship once we figure out her dog Rambo (also played by Lauren) is sentient. Later, their relationship is complicated by a pregnancy and the sort of drama you would expect in a compelling romance. Rambo's a dog though.