ToeJam & Earl
TJ&E is one of the quirkiest games I've seen, which is only one of the reasons I think it would make an awesome DS remake. It's awkward at first, avoiding enemies rather than fighting them, and the movement seems slow. But it didn't take long for the game's general oddities to grow on me. This is one of only a few games that manages to successfully combine off-the-wall humor with working gameplay devices.
Co-op works really well, and there are some devices here that still seem ahead of their time. With one player as ToeJam and the second as Earl, if the two move more than one screen away from each other, it bisects and becomes split-screen play. When players are nearby they can also share items and health.
As an adventure game, TJ&E looks like it can be really hard and take forever (no form of game-saving here). But even if you never finish, it's worth playing just to witness the zany items and ToeJam and Earl's hilarious banter.
Progress: Gave Up -- Level 11