Rewind
I have an idea for a game, but no time to implement it, so I’m going to throw it out in the hope that some interwebby young’un with time on her/his hands will build it for me (and everyone else). The starting point is a basic first person shooter with a science-fiction theme (rayguns, jetpacks, etc.). What makes it different is that each player has the ability to wind time backwards, but only a little bit: at any point, they can press a “rewind” button and reverse the flow of time, but doing so uses up the charge in their temporal battery (which is fairly limited). So, if you just got shot, you rewind a few seconds, then go forward again, but this time you don’t stick your head up to look over the parapet. Or suppose you missed a shot: no problem, wind back a second and aim a little lower.
Ah, but wait. If you’re winding time backward because you just missed a shot, I’m going to do something different in th replay as well, right? I’m going to jump instead of crouch, or crouch instead of jump. Except you know that, so instead of aiming low where I was crouching, you’ll aim high because you know I’m going to jump instead. But I know that you know that et cetera, so it becomes one great big head game:
There are lots of ways to mix this up—power-ups that recharge temporal batteries, for example, or being able to spend temporal energy to force play forward, canceling out someone else’s rewind—but the basic mechanic is pretty simple. Implementation will involve more than just recording and undoing events in a standard FPS (if I jump off a cliff, then start running when I land, the game will need to insert an “undo falling” event between the jump and what comes after), but I think that’s a simple matter of coding. Bonus points if the characters look like the robot from Chronotron 
Not quite sci-fi themed, but check this out: http://braid-game.com/
The main feature of the game includes that you can go back in time by holding shift. The ways in which you do so vary and get more complex as you progress through the levels. Awesome game.
(It’s also not FPS. But that would be awesome.)
Braid, as Liz links above, is also one of the best plots in any videogame ever if you follow it through to the end. (No spoilers.)
Oh and the music is fantastic.
There’s also TimeShift: http://en.wikipedia.org/wiki/TimeShift
What I’d be most interested in would be how do players resolve those meta-traps. You know that I know that you know that I’m going to shoot you in the next second. What do you do? And what is your new learned instinct after going through plenty of iterations of this over an hour of playing?
Jorge, I challenge you to a game of rock-paper-scissors!
I accept the challenge! Though like Hector against Achilles, I know the outcome even before we start.
While the idea may seem interesting, I would imagine that the game play would turn out to be quite frustrating in a multiplayer game, as players might be getting thrown back too often in time, even when they don’t have anything to do with the action…
FEAR (the game) had a multiplayer mode with bullet time, but where only one player at a time could activate it (one had to posses some powerup that you could find or take it from the player carrying it by killing him), and my personal experience was that even that already impeded on the fluidity of the game for most players.
So I think that a game where all players can activate an actual timeshift (and not just a time slow as in FEAR) might actually end up being more frustrating than fun, in average.
That being said, it would certainly be worth prototyping such a game, and I would think that the programming behind it would be quite interesting.
And while looking at TimeShift, here’s a quote from the lead producer: “The first idea was to have Time Shifting work just like in single player. Sounded great on paper, we even figured out how Slow would be trumped by Stop and Stop by Reverse. Ultimately there were two primary problems… One; it sucks to have 15 people frozen in time while one person runs around; we called it Fun For One. The second problem was what reverse looked like… Lag. Even though the game was doing EXACTLY what it was supposed to do, the other people going in reverse thought the game was lagging out since they were telling it to do something and it wasn’t responding.”
http://pc.ign.com/articles/799/799795p1.html