Lara Croft and the Guardian of Light
I haven't played any Tomb Raider game for more than ten minutes; the franchise is meaningless to me. But I heard that Guardian of Light was a neat little co-op title, and upon further investigation, it is!
It has qualities in common with Trine -- specifically, that each player (though there are only two) has unique abilities that must be used to progress through the level, and which can also be used for hilarious griefing. It also has qualities in common with a two-stick shooter, since that's basically how the combat works; there are no melee attacks, just guns (plus a throwing spear for Totec) and remote-detonated mines. There are also some RPG-ish elements, as each player equips guns and enhancement items found in the level, or earned by completing skill challenges.
The challenges are an interesting twist on the otherwise (generally) simple level design: collecting hidden items, finishing an area in a certain time limit, reaching a certain high score (although this is broken in co-op, as it only counts one player's score, even though by necessity two players work against each others' scores), or even more esoteric things like crossing a river without touching the water. The game always makes the goal fairly clear, and the plot isn't really interesting at all, so interrupting it to follow a wacky, optional on-screen prompt is actually a lot of fun.
It's longer than I expected, and probably longer than it needs to be; I feel like we reached the full depth of the game's mechanics several levels ago. But what is here is pretty satisfying, from a chase scene with falling platforms, to boss fights against dinosaurs, to a Zelda-esque dungeon where we had to do puzzles to collect eight key items. And the basic gameplay mechanics that Lara and Totec use to cooperatively solve puzzles are just cool.
Progress: Level 12 (co-op)