I play Animal Crossing for plenty of reasons!
First, I love the atmosphere- the calm, lackadaisical vibe of just moseying along in a small village. I love the sense of belonging it gives you. Walking around well it's raining in-game... you plant flowers and check on your neighboring cat whilst deciding whether or not you want the windmill to go in the woods or on the cliff... it just feels wonderful. From the K.K. performances on Saturday to taking a moment to write a letter for a villager, it just feels great. I've always loved stuff like that.
Second, because of reason one, Animal Crossing is calming. It not only satisfies my creativity (and more or less control-freak nature) but it brings me down to earth. Everything feels simple and slow again.
Third, Animal Crossing has almost become a part of my personality over the many years I've played it. The vibe of the game and its aspects fit me so well, I can't really see me not playing it. To put it blatantly- it makes me happy.
There are a few other miscellaneous/personal reasons why I love Animal Crossing, but these are the most prominent.
I apologize for the length of my ramble!