Alice Tsukagami (Bloody Roar)
One of the stalwarts of the Bloody Roar series, which saw human fighters with the ability to transmogrify themselves into enormous anthropomorphic beasts, Alice's alter-ego was an enormous, insane-looking rabbit. For some reason the rabbit kept her tiny jacket, possibly because it was always a bit nippy in the arena.
Robbie the Rabbit (Silent Hill 3)
A bit of macabre entry, this one. Robbie's regular appearance in the Silent Hill games following his debut in SH3 is something of a mystery. A pink-furred anthropomorphic bunny with a ghastly, bloodstained mouth, Robbie is something of an homage to the sketchy nature of bloodied rabbits in horror films and the creepiness of human-sized mascots in general. He's just there to tenuously tie games together in loose fashion, and freak players out by just being there. Watching.
Oswald the Lucky Rabbit (Epic Mickey 2)
Poor Oswald. After all of the hurrah surrounding his return -- the salvation of one of Walt Disney's forgotten originals and a long lost rival to Mickey's throne -- not even Oswald and his super conveient, electricity-controlling remote could save Epic Mickey 2 from being a pile of tepid mediocrity
The Celestial brush god of the moon, Yumigami is a bunny with a penchant for rice cakes, hence the mochi mallet. She's not ooverly fond of Amaterasu, but she does bestow the ability of Crescent upon him, which allows Amaterasu to turn day into night and vice-versa.
Jazz (Jazz Jackrabbit)
Nintendo had a fat plumber. SEGA had the Blue Blur. The PC had a bandana-toting rabbit with a chip on his shoulder. There were actually a fair few similarities shared with Mario, to be honest. Jazz, too, was out to rescue a princess (Eva Earlong of the planet Carrotus) from the clutches of a shell-wearing evil mastermind -- the tortoise Devan Shell. The only real difference is that Mario felled his enemies with his feet and his arse, and Jazz had a sweet blue blaster instead.
Rabite (Sword of Mana)
Rabites are to the Mana series what Chocobos are to Final Fantasy, only you can't ride Rabite. Well, you could try, but you'd probably squash it. These bodiless bundles of fluff have rather become the mascot for the Mana series since they first appeared back in Sword of Mana/Final Fantasy Adventure on the Game Boy. In Legend of Mana you could breed them as pets.
Marquis de Hoto (The Night of the Rabbit)
There's something irresistible about The Night of the Rabbit to someone who grew up on a steady diet of the fantastical adventures peddled by the likes of Tolkien, Lewis, Carroll, Gaiman, and a certain A.A. Milne. The Marquis de Hoto is an intriguing character -- a perfect mystery at the heart of Daedalic's adventure game -- who could have stepped out of any number of fairy tales. He's also a dimension-hopping rabbit in a top hat.
For some, they ruined the Rayman series and will always be something of an abomination, but for others they're a pretty funny sideshow that's allowed Ubisoft to pump out a whole bunch of amusing family party games. The Rabbids are basically Ubisoft's Wario.
Fran (Final Fantasy XII)
If Balthier is Final Fantasy XII's Han Solo, then Fran is that game's Chewbacca...only somewhat less hairy, slightly more Amazonian in her proportions, and with bunny ears. If ever a role screamed cosplay...
Fran is technically not a bunny, or a human for that matter. She's a Viera, which means she has exceptional hearing (so much so that she can hear the voices of spirits) and Mist is like violent catnip to her.
"Do a barrel roll." Legend.