Ahh, Contact. God, I love this game for some reason. People call it a spiritual sequel to Earthbound (probably due to the oddball humor/story, probably also due to a baseball bat being a weapon), but I actually like it. It reminds me of an MMO in a way, though purely single-player. Everything levels up naturally as you use it (like, you move faster the more you walk, the more you take damage the higher your defense gets) and the outfits have their own little bonuses too.
I like the disparity between the screens in terms of art. The Professor and Mochi are all pixelated and Terry is all smooth-looking, and it even transfers over when they're on the same screen. Hehehe.
Never did WiFi, but all the same you can't really play with other people, though that'd be an interesting thing to have had in place.