Lego would be the obvious first choice, but any dungeon crawl would be good too. The X-Men franchise is fun. It’s like an advanced lego game for grown-ups. Not that it’s adult or anything, just that it involves more interaction than the extremely basic lego series. I don’t recall dying being a huge issue, but we played it with between 2-4 players who were all capable gamers so it’s possible it would be. (The first two to arrive would start with X-Men while waiting for the 3rd and 4th to show, play for a little longer once all four were there and then switch to Madden or Halo.)
Halo is pretty darn macho, but it’s got a fantastic no-penalty-for-dying coop mode. My buddy and I had a lot of trouble getting into Gears of War and that newest zombie game that just came out recently because as soon as one of us dies we’d have to restart the very long levels. Boooo! Didn’t Halo fix this genre? What’s up with the throwback search-for-healthpack paradigm where effectively when one dies all die?
With Halo, you cross checkpoints every few minutes, and whenever one player dies the second simply has to run to a quiet place and the dead teammate will respawn. You lose your weapons, but you lose your weapons all the time by running out of ammo anyway. Plus if you can get back to where you died your weapons will be lying there waiting for you to pick them back up. And there are no stupid healthpacks to look for. As long as you don’t die, once you stop taking damage for a few seconds you heal automatically.
Once Halo 2 came out my buddy got much better than me at most games, since he plays online while I do not. Halo coop was a perfect solution for us. I could run in guns blazing against a horde of enemies, get killed, respawn, run in again, and keep repeating until all the enemies were dead. He’d hang back in a more reasonable location taking on manageable levels of enemies. What fun is that? heh.
If both players die you restart from the last checkpoint, which is almost never more than a few minutes back in terms of gameplay.
Halo 2’s coop mission kind of sucked. I don’t know if you can physically play it or not, but if you can the original Halo coop is the bee’s knees. Not sure about the newest one. My buddy doesn’t like it because it doesn’t support 16:9.