the only title I can imagine which sports funny animal characters throughout would be "Usagi Yojimbo" by Stan Sakai. other manga titles with animal characters center rather on mythical stories and appearances than everything else (like "Inu Yasha"). some anime title which should have spawned also some maga titles is "Hyper Police" (author unknown) which has a couple of furry characters, and shapechangers.
"Bucky O'Hare" is also an animated title which has spawned a single-issue comic book telling the first run of the series. as far as I can tell from the couple VHS I stumbled across, the comic is nicely drawn, the cel-shade colouring is nice to look at, and the art itself is playful, and very close to the animated's style. personally I'd recommend both if you cared for animated series.
europe has a rich franco-belgian comic culture, of course including funny animals; sometimes they tell not-so-funny stories, even downright serious and even sad. I don't know how many of them are published in the US (besides "Blacksad", film noir made comic); if it helps you I might go and search for their original french titles, so you can pilfer through amazon's book stacks for them.
a couple years ago I met a japanese artist studying european art styles in germany, and he had some of his own comic with him, of course in japanese original... I don't speak japanese, much less can read it, but what I saw looked nice and thought-out (the story seemed to make some sense to me, even.

) I have lost contact with him now... so I can't tell where he has his stuff published.
his name is Sasaki Daisuke, btw. if perchance his comics are published in the US I would appreciate a note... ^^