Ok so.
If you want a wolf game, specifically, there are several, but this seems to be the best.
- Wolvden is good if you want a realistic experience, but it isn't the easiest. It has a bit of a learning curve and takes a lot of time out of your day. Depending on your schedule, you might not be able to play it and Lorwolf at the same time.
- Wolf Play is a decent game; the worst thing about it is that there's no way to stop wolves from aging, so if you take a break, your wolves might be dead when you get back.
- Wajas is great if you like the customization aspects of Lorwolf. It revolves entirely around making and dressing up rainbow wolves. It's not a difficult game at all, although complicated projects may take a long time to achieve, and the wolves don't age.
- Google knows of more wolf games than I do.
There are also horse games and dog games, the two largest categories. I recommend Furry Paws as a dog game; it's very realistic and revolves entirely around the breed and show aspects, but has a large, active community and cool events (Christmas, Easter and June being the main ones). Its learning curve is low and you can leave dogs locked indefinitely to prevent them from aging.
More info on horse or dog games if you want it (ping me!)
For a wild animal game your best non-wolf options are Lioden for lions (with the same caveats as Wolvden, although it's more extensive and has fewer bugs) and Wild Horse's Valley for horses (the base game is finished and more features are in development; it's a long term game and gets grindy toward later levels, but the artstyle is magnificent. Built around exploring the valley. You gain and lose herdmembers pretty freely as you explore, so it's not a game for people who get attached to every individual horse).
Felisfire is a sci-fi cat game with a largish playerbase. It's a little odd to play, but you can do lots with it: breeding, color alteration and dressup, exploration. It's sort of like Wajas with cats.
There's probably another cat game out there somewhere, but I don't think there are two. Cyska Siberians still exists but requires Flash, so don't bother with it.
The only goat games I know of are Goatlings (a really cute fantasy goat game which mainly revolves around acquiring items. The game is impossible to lose and easy to get ahead in, but the playerside economy is severely broken due to many, many permanently retired items) and Ropin' Ranch (a realistic horse game with goats and cattle. No fantasy elements, still in development.)
The main rabbit games are Leporidae (with an old version at classic.leporidae.org, which I believe is still taking signups) and the wild rabbit game Warrenz, by the same developers. Both Warrenz and new Leporidae have a weird exploration mechanic which rewards items. You can breed bunnies in normal or fantasy colors, and both versions of Leporidae have an option to hide fantasy colors entirely. Warrenz also has a combat system.