One of the options for PCs or NPCs in The Dresden Files is a shapeshifter template, which have a normal human form and any animal the player and GM can decide on. The "standard" example is a werewolf (because one of the editors is a werewolf), but were-ravens and other exotic examples are discussed in some detail. Bob takes exception to calling them all "lycanthropes" (claiming that "theriomorph" is a more accurate word), but Dresden shoots him down on the grounds that people understand "lycanthrope".
D&D uses the term lycanthrope to refer to any sort of werecreature (though the second edition Monstrous Manual acknowledges the misnomer, and suggests "therianthrope" as an alternate name). There are multiple varieties of lycanthrope aside from the usual werewolves, werebears, wererats, weretigers, wereboars, dire wereboars (hill giants that turn into dire boars), and jackelweres. The 3.5 edition monster manual even has a template for any animal. They've always been able to take on the normal animal form and infect with a bite, but other details have cropped up with the evolution of the game, including the addition of a "hybrid" form equivalent to the Man-Wolf, the existence of natural lycanthropes in addition to infected ones, and the imposition of a whole new alignment (and personality) not just on the nonhuman forms but on the human(oid) as well. The most recent edition has the Lycanthrope template, allowing one to make were-anything characters. Recent publications introduced the Shifter player race, descendants of humans and lycanthropes, who were effectively "lycanthrope-lite".
Mystara has Chevall. The centaurs who turn into full horses at will and can be hurt only by silver or magical weapons and... that's all.
Van Richten's Guide to Werebeasts is an AD&D 2nd Edition, Ravenloft book with a host of rules on werebeasts. Unlike most settings, lycanthropes in Ravenloft are almost universally evil, except for the Lawful Good wereravens.
The tibbits, introduced originally in Dragon magazine and reprinted in the Dragon Compendium book, qualify. Their humanoid form is small, with Pointy Ears and cat eyes, somewhat resembling halflings. They can turn cats at will.
Dragon magazine also included a sillier variant in the form of the werehare. Among other things, the creature could only be harmed by magic weapons and holy hand grenades.
The old Night Howlers supplement for the boxed set/Rules Cyclopedia edition of D&D actually presented rules for weres as player characters in the Known World (Mystara). Notably, actually acquiring the full powers and immunities of "normal monster" weres took time and experience points and the ability to transform into a hybrid "beast-man" form only came at fairly high level after that. The book also explained the ultimate cause of lycanthropy in the setting as a magical virus that escaped from an Alphatian lab in ancient times — a literal case of A Wizard Did It.
Another 2e lycanthrope were Lythari, who are what happens when this trope crosses with Our Elves Are Better; they're Chaotic Good silver-hued planar elves who can naturally shapeshift into silver-furred wolves and back, who dwell in hidden pocket planes and forests that lie between worlds. They were introduced in Planescape, but are more associated with the Forgotten Realms.
Werefoxes, also known as foxwomen and werevixens, are a 2e edition One-Gender Race lycanthrope who appear as elven or half-elven women with silver hair in their humanoid form and silver-furred humanoid vixens in their true form. They're an evil, selfish, hedonistic race who are sterile, and reproduce by infecting human, half-elven or elven girl-children with their disease, causing them to become werefoxes upon adolescence; non-elfin "daughters" become increasingly elf-like after the infection takes hold, until eventually they are pureblooded elves, in terms of looks.
As if the wereboars of common 2e weren't enough hog-shifters, Mystara included wereswine — Chaotic Evil gluttonous shapeshifters who alternated between the forms of indulgence-fattened humans and huge common pigs with a massive appetite for human flesh. And they didn't replace wereboars in Mystara, either; both species coexisted... and hated each other, striving to hunt, kill and eat one another wherever possible.
Fun fact; the most ancient lore for the legendary Demon Prince Orcus actually declares he was a wereswine in his mortal life, before he died, went to the Abyss, and clawed his way to the throne of Demon Prince of the Undead.
The incredibly large array of 2e lycanthropes after the aforementioned consists of: werebears (iconic for being one of the only good lycanthrope strains), wereboars, werecrocodiles, werehyenas, werejackals, three varieties of werejaguar (normal, Mystaran, and Ravenloftian), wereleopards, werelions, werepanthers, wererats (with more powerful "wererat lords" leading them), wereravens (the only other good-aligned lycanthrope), wererays, weresharks (two varieties; normal and Ravenloftian), werespiders and weretigers.
Another Dragon article introduced giant lycanthropes. In addition to some giants being susceptible to infected lycanthropy, there were also two natural giant werebeasts; the shadkyn (voadkyn/mobat) and the polarwere (frost giant/polar bear, and unlike the regular werebear, evil).
Exalted features the Lunars, who are technically werebeasts in that they have one totem animal they strongly identify with and can easily shift to — but then again, they can shift into anything if they drink its heart's blood. Two of the signature Lunars (Red Jaws and Ma-Ha-Suchi) are technically werewolves, but if you go by signature characters alone, you've got wereowls, werecats, werebulls, wereorcas...
With Innistrad and its accompanying marinade of Hammer Horror tropes come Werewolves.
The Munchkin card game gives us a werepenguin, a werehamster and a weremuskrat. They are all oversized and sharp-toothed - even the penguin has fangs.
The Old World of Darkness' Werewolf: The Apocalypse, in addition to the titular werewolves, has 11 other breeds of shapeshifters, described in their own Splat books. Some examples include the Corax (were-ravens), Gurahl (were-bears), Bastet (were-cats), Rokea (were-sharks), Mokole (were-lizards), Kitsune (were-foxes), and Ananasi (were-spiders).
The New World of Darkness also has werewolves, and provides tools to build just about any wereanimal you can think of (in Skinchangers, Changing Breeds and War Against The Pure).
Pathfinder, being essentially "Dungeons & Dragons 3.75", naturally includes the iconic D&D lycanthropes in its lineup; the Chaotic Good werebears, wereboars, werebats, werewolves, wererats and weretigers.
Rifts and other games in Palladium's Megaverse have them as multiple species, ranging from Wolves to Bears, and some of the big cats such as Werepanthers and Werejaguars.
In The Splinter playable races can all shift between three forms at will. In fact, the ability to shape shift is treated as a sign of sentience in The Realm.
Warhammer Fantasy doesn't mention them offer, but there are a few, apparently; there's quite a few werewolves and werebears living in the Northlands — in fact, lycanthropy (in the "turn into an animal/man-animal hybrid at will" sense) is one of the older Chaos Gifts. Another is to become a "Chaos Were" — a mutant who can assume a human form, but then revert to their usually far gribblier true form when danger threatens.
In the GURPS Supers supplement Wild Cards, Sewer Jack is a were-alligator.
Bleak World has the werebeast as one of it's PC races. In addtion to the standard werewolf, they also have Were Cats (Which are stuck as half cat/half human hybrids) at all times, were-cockroaches, and were-fish (which are the hardest to play as)