Well, Wizards released an entire web enhancement devoted to cats as an April Fools article, which has a lot of cool options for cats. It does have at least one “playable” cat (Cheshire Cat, to be exact), but it’s not really a very playable option because it has LA +3. If it lost the DR, toned down the ability score bonuses a bit, it could possibly pass as a more playable LA +1.
The more typical answer to the desire to play as a cat is to use the tibbit race from Dragon Compendium. These shapeshifters can take on the form of a housecat, and are an LA +0 race (i.e. in line with the regular races). In their regular form, they are Small, have −2 Strength but +2 Dexterity, and Darkvision out to 60 ft.
Catfolk are in Races of the Wild, but they’re fairly disappointing. They have LA +1, and get very little to show for it, sadly.
Shifters from Eberron Campaign Setting or Races of Eberron are quasi-lycanthropes that can “shift” or become more bestial, with fangs or claws or what have you. Could be somewhat feline, but mostly it’s just humanoid with claws etc. They are LA +0, but tend to be fairly underwhelming even for an LA +0 race: while shifting, they’re pretty typical, but that means when they’re not shifting, they’re sub-par.
Both tibbits and catfolk can probably qualify as “feline” for the purposes of the feats and similar in the Fabulous Cats! article. Shifters could if you let them, I suppose.
As for homebrew, bhu has a fair amount of kitty-related homebrew, and he’s a fairly noted ’brewer. I haven’t personally read any of his cat stuff, though.
In Enemies of the Empire, starting on p244 there are rules for "Shapeshifters" and "Child of Chikashudo" advantage. On 246 they have a sample Kitsune so you know which shapeshifter powers/aspects are typical for the race. The option is more general because there's so much history in other books for what was once a minor clan, and because so many other creatures fall under the same category.
Best Answer
Tabaxi are a playable catfolk race presented in Volo's Guide to Monsters.
Beyond that, you're looking at creating a custom race, as described in the DMG at pp.285-287. Or looking for some second-party content, perhaps over at DM's Guild.