Animal Crossing

Animal Crossing is a very unique game, one of the most ever actually. It starts off with you arriving in a town (which you name at the beginning of the game, along with your character's name) via a train. Right away you aren't attacked by monsters, you don't gain exp, and you don't fight any bosses. You live life, as you see fit. You can pretty much do anything you'd like, from catching bugs, to going fishing, to even getting a job. The game features a huge list of features including:

Uses the Gamecubes clock and depending on the time and date things will look different and different events will occur

Depending on the date the 4 different season will occur, and it will snow in the winter and leaves fall in Autumn.

You can make friends with other members of your town.

There are tons of different clothes that you can wear, tools you can use, and you can even buy your own house.

You can exchange your character to your friends' game and live in their town.

You can play old NES games on your GC (the full list of games can be found at the end of the preview) or even play them on your GBA (no cartridge necessary).

You can collect different things like fish, bugs, etc.

Up to four players can live in your village (but you cannot play simultaneously)

So you see, there is tons of interaction and things are constantly happening. Holidays even happen such as the 4th of July (fireworks and all). Since the game runs off the GC's internal-clock things are always happening, if you don't check back for a while your friends will feel neglected. While the graphics aren't the best they look good and are improved from Animal Forest + on the N64 (which didn't make it to the US).