From this gallery page, http://sonamyfan362.deviantart.com/gallery/41694107, A New Life Era (story) and Moe and BIOS birthday party heavily speculate this between between Amy Jr. and Moe. The Recovery Part 2 shows there MIGHT be some romantic love between the two. However, they're both very young, and may not be each other's soul mates. For all we know, Bertha might be Moe's soul mate, although The Hacker probably wouldn't be too happy about that.
Chip 'n Dale Rescue Rangers itself already provides a setting with so many species in the same society that Interspecies Romance cannot be avoided, also because the lead characters Chip and Dale are the only chipmunks in the entire setting. While the series itself doesn't go much beyond some swooning and flirting as far as the Rangers themselves are concerned (except for Monterey Jack who used to be engaged to another mouse), Fan Fiction does, and a lot so, while still avoiding flat-out Shipping fics. It usually builds on ships already hinted at in the show.
Also quite frequent is the "Pro" one between Chip (chipmunk) and Gadget (mouse). "Pro" fanfics are more common than "Anti" ones which ship Gadget with someone else or have her prefer celibacy to a relationship with Chip.
While Dale and Foxglove can be seen as a couple at the end of "Good Times, Bat Times" already, Chip and Gadget usually don't start out in a relationship at the beginning of a fanfic or a new Fan Verse. Fics and even 'verses like the idea of letting the actual romance grow by itself (for example Fly to the Light) or leaving one or both heartbroken because they Cannot Spit It Out and putting one or both through the wringer before their deserved First Kiss (for example Rhyme And Reason, Of Mice And Mayhem, half the Midnightverse).
Of Mice And Mayhem is a special case. Chip and Gadget are strongly in love with each other, and they do come closer, but only as close friends because neither wants to take the next step due to genetical incompatibility. Especially Chip thinks that Gadget might want to have children one day, and that she'd better wait for a mouse guy. Later in the story, while Chip is still in Washington and the national mascot, Gadget performs a DNA check on herself on the background of the events of "A Fly in the Ointment" when she switched bodies but not heads with Dale, and she discovers that there is still enough chipmunk DNA left in her to make her compatible with chipmunks. Dale and Foxglove, on the other hand, simply don't care, or they don't want kids.
Next to Dale & Foxglove and Chip & Gadget, The Midnightverse hints at something growing between Sparky (rat) and Lahwhinie/LaWahini (mouse). Diamonds In The Desert reintroduces Clarice from the Chip N Dale cartoon "Two Chips and a Miss" who plays with the two 'munks, but who also is the crush of a mouse. It also introduces a third rat who looks a lot like Rat Capone and Francis (they're brothers in this 'verse), and who hits on Gadget a lot.
It is said that The Untold Ranger Tales haven't left out a single possible straight pairing among their characters yet, and they're as multi-species as CDRR fanfics come.
Zim and Dib (Irken/human) are by an enormous margin the most popular pairing in fanfiction, due to perceived Foe Yay. Less popular variations include Dib and Tak (human/Irken), and Gaz and GIR (human/robot, though granted he did show signs of having a crush on her).
There are tons of stories out there of human / pony romance. So many, that this story was able to successfully Meta Twist the reader by having this not be the case. Just check the comments: every single one points this out.
Teased in The Commander Of Shepherds between (female) Commander Shepard and Luna. The potential pony/human squick factor is lessened by Luna being a shapeshifter.
In Summer Days And Evening Flames, Gilda (a griffin) eventually starts dating her guard captain Iron Bulwark (a pony). She's justifiably worried that dating him could make others look down on him, considering his best friend is very racist to griffins.
Kalash93 has a number of stories which include this.
Twi and Me has human male and female pony (Twilight Sparkle).
Xenophilia, involves Rainbow Dash getting a human boyfriend. Despite being a Lemon the fic spends a fair amount of time discussing differences between humans and ponies as come to sex and gender relations. It mostly treats the human as the alien partner (talking about his Exotic Equipment, for instance).
A pair of recurring background characters in Cadence In A Minor are a stallion/griffon couple, who are also soldiers on the opposite side of a tense border. Despite everything stacked against them, they make a pretty cute couple, all told.
The Reading Rainbowverse has the typical Gilda/pony romance... but mixes it up by having a cat crush on Gilda too. Not an anthropomorphic cat... a normal housecat.
The Mixed Up Life Of Brad has this between Brad the human, and Twilight the unicorn. Subverted a bit, as Brad fell in love with Twilight when she was transformed into a human, and now that she's back in her pony form he finds her physical appearance unappealing. It is noted that they cannot ever be truly happy together, being so different from each other.
The same author's A Mighty Demon Slayer Grooms Some Ponies gives Danny (from G1 My Little Pony), an eleven-year-old human, a crush on Surprise the pegasus (who is an adult at the time by pony standards.) Nothing comes out of it, and he still has bad memories years later. It's hinted that it's all because he was still a young kid at the time, confused by his budding sexuality.
In Arads Stardust, it's fairly common in Equestria, in part because there are an average of 3 stallions to every 7 mares. Upon hearing this, Lana immediately figures the best way get Twilight off the fact that she's XCOM's newest test subject is to imply that Matt thinks Twilight is cute. She takes it very seriously, and even searches for information about "Human Courting Protocols." Matt is mostly upset how Lana refuses to stop teasing him about it, but there is some Ship Tease between the two.
The Kirk/Spock pairing from many a fanfictionnote also the Trope Namer for Slash Fic. Kirk is human, Spock is half-human, half-Vulcan.
The pairing of Captain Picard and Q is rather popular in fanfiction. Picard is a human, and Q is a transcendent energy being. Much drama is made of the fact that Q is a hyper intelligent and virtually omnipotent being that finds Picard a fascinating mortal to mess around with, and Picard's annoyance at Q's antics.
Although the fanbase for this pairing dates back somewhat to the 4Kids series, Donatello and April O'Neil has had a wave of momentum lately because of Don's crush on her in the Nickelodeon series, spawning numerous fanfics and fanart, Another popular couple inspired by both 4Kids and Nick eras are Leonardo and Karai.
Fans of the 1987 animated series have Donatello/Irma, April/Michelangelo, Michelangelo/Kala, and Leonardo/Lotus Blossom.
The Sirens of Azeroth suggests that the many species of Azeroth don't have a huge amount of trouble with, at least, casual interspecies romance/intercourse, demonstrating among others a Dwarf/Draenei (seven-foot faun-like blue alien) relationship, a Troll/Blood elf lesbian couple with an open relationship, and a pair of tiny gnomes talking about how their favorite types of 'men' are Tauren (hugeminotaurs), though they could just be making that up.