I've played a lot of pet games in the past but Mweor is one that I always come back to.
Its been around for a long time (since '08) and is about breeding and leveling up 'mweors', cat like creatures. They come in a variety of breeds and there are a lot of markings that can come in any color! Best part, they don't die! Even if you don't feed them! They do get too old to breed/level, unless there gen 1, or custom. I tend to get more attached to my gen 1's for that reason.
Its just a really fun game that I hope stays around for a long time. Be sure to check it out if you haven't!
Mweor!