To me, Animal Crossing is a means to escape from myself for an hour or so during the day. I deal with a lot of anxiety in my everyday life, so to be able to put my energy into something small, peaceful, and undemanding is wonderful indeed.
Animal Crossing has become a stress reliever. I have a illness so I tend to get exhausted or ed ridden alot, so AC has always found a way to keep me company. It also helps with my anxiety and depression. I've seen many people say that it helps with their depression, and I do agree. It's a nice paced game, no stress, so it's something that I couldn't ever let go of.
Nostalgic. I've been playing Animal Crossing since it came out on the Gamecube when I was little. The experiences you get from playing AC are very memorable and can feel pretty rewarding, which is one of the bigger reasons why I think it should never be underestimated.
I find that AC:NL in particular is very helpful when I'm having an off-day. It gives me something to look forward to. I like hearing what my villagers have to say, and I enjoy celebrating special events with them. When I'm having trouble falling asleep, I go to the dream suite and visit some of my favorite towns, or I go fishing on the island. When I'm trying to stay awake in the morning, I start up my game to see what's going on for the day. And to be honest, the AC world is probably the only world where I'm much less likely to procrastinate.