What a neat thread idea,
mollyig! I have lots of little animal obsessions, rather than one big one.
Cats - this is a "duh" one, because I'm a cat person and there's never been a time in my life when I didn't have at least one cat as a pet. Right now I'm a foster mom for abandoned/abused cats. I have a cat calendar, and a couple little candle-holders and things, and of course a grey cat named Spike who is currently sleeping at my feet.
Hummingbirds - My nickname in college was The Mighty Hummingbird (it's a long story, don't ask) so ever since then I've had a soft spot for them. I've got a hummingbird poster and am working on a hummingbird cross-stitch to hang on my wall. My personal web site, back when I actually had one, had a hummingbird theme.
Pigs - Just stuffed pigs though. I think they're cute. My high school boyfriend got me one as a gift one time, just an out-of-the-blue present for no reason, which was pretty much the only nice thing that jackass ever did for me but that's a whole other story. He (the pig) is my favorite stuffed animal and he always travels with me. My parents brought me another one not too long ago from a trip to Chicago, and now the two pigs are inseparable. I think they tell each other jokes when I'm not in the room.
Frogs - There was an "incident" in college where I heard a frog cry - yes they actually cry, has anyone else ever heard them? - and it sounded horrible and I felt so bad for the poor frog, and ever since then I've really liked the ugly little things, unlike Willow.

It's mostly residue sympathy, I suspect.
As for W/T, other than the obvious "cat" answer, I can see Tara having an obsession with graceful animals, like dolphins or swans. Or perhaps mythical animals like dragons or unicorns or mermaids (heh heh). Willow, of course, likes dogs. I also think she has a soft spot for wolves (left over from the relationship with Oz) and maybe a stereotypically "smart" animal, like owls. Or duck-billed platypuses, just 'cause they're the "outcasts" of the animal community and Willow would feel sorry for them.