Animal Crossing Wild World
This real life sim makes yet another return, this time using the DS features to improve the game. The general idea of these games is that you get sent to a town, which is randomly generated by the game, and have to get richer, improve your life and virtual house and collect various things such as insects, fish and fossils.
There are many ways in this game to customise the game as if you were really living in your town, from changing objects around in your house (and using various sets of furniture to decorate it, from space to rustic cabin. And yes, you can take part in some fishing, collect rare items and trade objects online by inviting people to your town (but don't get scammed!)
It makes use of the game wifi mode by allowing you to invite people to your town and talk to them via a very clunky keyboard interface, plus trade items and other stuff. Note though they have all the powers you do, such as being able to cut down trees, buy things and the like, so it may or may not be a good idea to give your friend code to random strangers.