Here's a brainstorm I just had if anybody wants to twiddle on the merits of it. A game in which the players must cooperate to achieve "victory" (the end of the game), but only one person is crowned the winner - not the person who wins first, but rather the person who was most helpful in getting other people to the end. So it's a purely competitive game, in that you want to beat the other players, but what you're competing in is just how cooperative you can be. Get it? (now's the part where you list 12 commercial games that do this)
I kind of think it could degenerate into a basic competitive endeavor in the end without the cooperation being really noticeable. But could there be interesting ways to make the competitiveness more sneaky, with an overt sense of actually cooperating? Certainly it would have to have no ways to backstab other players, but it would be fun if it were possible to screw other players out of being able to help you somehow ("oh, you want to lift me up onto the ledge? Don't worry about it, I've got a rope right here!"... and better yet, the rope flings you up another ledge higher, so you can then lift the other guy up!).
Maybe the best plan would be for each player to draw a secret goal at game start. You all have the goal of completing the game together, but maybe one of you has the personal goal of helping the most people, another has the goal of getting there last, one of getting there first, one of collecting the most blueberries, or whatever. Kind of a change from the original concept though, but at least it keeps the competition more secretive.
Note1: This isn't a game I'm considering, just an odd concept I was bouncing around, thought I'd share, steal if you want.
Note2: I'm new to this forum, and new to board game design, so hi! I've been making computer games for years (buy them, NOW, at the website below! NOW) and recently got really interested in board games more. I've always had an interest, and played various ones occasionally (like the endless hours of Talisman in my youth!), but voila, Carcassonne claims another victim.
Well, in essence I was thinking more along the lines of a "theme" of cooperation, since you aren't cooperating in a true sense. But imagine a game where the players all win or all lose - I keep having a vision of a mountain climbing game, so use that. You all win if you all make it alive to the top. If anyone dies, you lose. So nobody wins unless you all finish. Your personal goal in such a game, if it wasn't purely cooperative, would normally be to get to the top first. I think it might be interesting if instead your personal goal was to provide as much help to others as possible.
I think that it would break down to being a competitive game, with just a different theme to your actions - like you said, moving the other pawns instead of your own (but hopefully not that overt!). The real trick I was mulling (briefly, but I thought it's semi-interesting to discuss) was how to make it more about true cooperation, but with that undercurrent of wanting to help out the MOST. And I do get that that's pretty much an oxymoron as you point out, but maybe there's some way to half-ass it.
It's like those people who give to charity, but feel the need to announce that all over the place. They're not really doing it for the charity, they're doing it for themselves, to feel smug. Just kind of an interesting part of human nature to delve into, although I think it would be codified to the point where it would have little to do with human nature except thematically.
It might sort of work though, as long as the goal that needs to be achieved is hard enough that cooperation is an integral part of reaching it - that way, you can't constantly prevent others from helping you, or you'll lose anyway. Your goal would be to get your help from a variety of sources, to spread out the points you're giving people, while of course helping others as often as possible. It'd almost be malicious cooperation like "Haha! Now I'm in position to lift you to the next ledge, sucker!" (which is indeed syntactically the same as "now I can kill your monster and get 10 points", but at least it helps the game get won as well, and I think it's a fun theme to it). Of course, that opens the door to "spoilers" who see they're not going to win, so they suicide and kill the game for everyone. In a way though, that would be the challenge for the leaders - can they help SO much that they can get a suicidal man to climb a mountain? It adds a whole new level to it!
Here's another theme for it: a suicide hotline where all the callers are the other people working at the hotline (come on, that is a seriously depressing job!). Now that's an interesting game! You only win if all the callers survive the night, but the #1 winner is whoever prevented the most suicides (the desire for suicide would be a game element, since obviously it's counter to the players' goals, except in the spoiler case... maybe there'd be Depression Points you have to dispose of or something). I am a fan of quirky settings.