Unless you're the type who wants to kill everything in sight, don't overlook this gem.
Most people would be pretty taken by how unusual Animal Crossing is. You live among animals in a small town that is different from all others in the world. Each town has a different name, residents, fruit trees, and layout from all others. There are a nearly infinite number of possibilities, which will make you want to go out and see everyone.
The town changes every day: new residents come in, old ones move out, trees grow, mail comes, and the seasons come and go. This makes every day a brand new experience. You also can do any number of things: fish, catch bugs, gather fruit, talk to neighbors, garden, make snowmen in winter, redecorate your house.... The list goes on and on. The animals have funny dialogue too: One minute, they'll talk about sugar-free sugar cookies, the next about penguins not being able to fly.
The only thing that really gets me is that after you pay of your house, there's not much point to playing the game anymore, since you can do everything you need in the time it takes to pay of your house. But other than that, don't overlook Animal Crossing.