Secret of Mana had a fun (yet buggy and abusable) multiplayer co-op, which was really really fun! I love that game, the sequels (if you count the PSX game) also has the same two player goodness, yet the game engines were different in a way that made them not as fun.
let me also remind you about the multiplayer options in Final Fantasy Games starting with number 4. The nice thing about 4 is that both controllers worked the same as the first player controller. That meant that either player could walk around, scroll text windows, buy things, or imput actions for any character. This was good because a two people could play and if one player was faltering the other player could step in and do things for them. This also eliminated the problems of the later games where you were stuck with particular characters, as well as the games with three characters giving an unequal playing something something, you get the idea.
The next couple of games had the option to set certain characters to each controllers. that was neat, because the "character is ready" tone was different for each player.
blah blah blah, I'm sure you all knew that already.
on the other end of the spectrum, the dramatic battle mode in both Street Fighter Alpha and Street Alpha 3 allowed two people to play cooperativly against one opponent. (example: player 1 controlls ken, and player 2 controlls Ryu, and they both do damage only to M. Bison, who is controlled by the computer.) I really dont know why they havent come out with a game exclusivly capitolizing on that. I think it should be Dan's game... Or a servebot game.
and now you know what i think. HUzzaah!