Yeah, not sure this idea can work that well - but with much attention and planning, it can be very unique and cool (and maybe even fun ) -

A game (platformer would be good) where you have to get a Game-Over as fast as possible.

The game can start in an extremely hostile environment (lots of pit-falls, insta-death traps, enemies etc); and later areas can get easier and easier - comfortable layout, extra lives pickups, invincibility powerups (all located in hard to avoid places of course)...

It's just an idea...
But can be interesting.
Sort of an 'anti-game'.

Good to remember that the idea of GAME OVER came from the arcade game industry where it was all about getting the player to put more money in the machine.
These days with most gaming going on at home there no real reason for it

..but it sounds like an excellent idea.

http://gmc.yoyogames.com/index.php?showtopic=362308

There's a game advertised on the cartoon network where you are trying to kill yourself in five minutes in an office setting.

However, your game seems more like the objective of a level is lose it. Doesn't sound like my kind of game, sounds a bit too "novelty" ish.

What if the objective of the game is to create a logical paradox?

How about a 3d game where you go into the door of a little shed and there's an immense world inside?

I really liked the concept of My Life as a King, the Final Fantasy game for WiiWare, because you are put in the king position (instead of the adventurer one as in every FF game). They removed the most tedious in RPGs, the battles. I believe that is brilliant, a game where you tell the adventurers "Retrieve the Sword of Hope from the Cave of Darkness, here you have these armours, weapons, tonics, elixirs and amulets" and they go, and a few days later they come back successful, hurt or with several members dead, they tell you where they reached, the different enemies and their attacks they faced, and whether they gained levels or not, and then you adjust the supply you give them to face the cave again (for example, giving them fire protection if they fought several fire elementals, etc).

Combat goes from something boring and repetitive (Attack, Attack, Item -> Tonic, Magic -> Fire, Attack, Attack, Item -> Tonic, Magic -> Fire) to something you cannot control directly.

Not that it has anything to do with the "kill yourself fast" concept (who remembers Karateka, the game where upon start, if you walk backwards you fall into a pit and die? 1''40 according to Wikipedia article), but it has to do with the "inverse" concept.

Another interesting story idea:

You play a goomba (the mushroom from Mario), and at the start of the game, you innocently play with your other goomba friend (as in, you move left and right, bounce into each other) - and then suddenly, Mario comes running from one side, hops on your friend (which gets flattened, and give mario 100 points) and keeps running on; leaving you in tears.

And from that moment, you search revenge upon Mario.

I've wanted to play that game. I've been designing a game with a similar concept. Battles happen, but you don't actually "do" the battles. While I was in the hospital, I got to document a lot of the idea to keep my mind off of things. I'm hoping to start programming the world engine this weekend.

Anyway, weird, unconventional ideas have a place in the market, but they're hard to pull off without feeling too gimicky.

My thoughts exactly.

Ugh, do you know those experiences:

Those are the most frustrating game moments, that make we wish you could control the response of the character after a battle. Johan, I can already feel my toes curling up.
But that aside, I had this sudden idea. I was thinking a Sonic level, where you often (react to) get on a higher platform for bonuses. Sometimes sequentially. What if you ever got higher picking-up bonuses and finally plummet to your death
Or pick-up a Mario-style flying item, only to gain height for your fall.
And I (unintentionally) came up with this story:
DarkMage: Muhaha! Princess now will never escape my trap! Princess: You are a fool, there are dozens of men who would want to beat you up and free me! DarkMage: Exactly! And your foolish father has declared anyone who does can marry you! Princess: No! No, I want to marry prince Edgar! DarkMage: Either way you're doomed! Muhahaha!
Then a hundred brave men come for the princess. Each must fail for the princess's sake. You get three stages to retry and each man is stronger (and more desirable) then the previous. Anyone can marry the princess, but the ultimate goal is letting the princess finish her captor. Notice how men are levels and stages are lives?

Whoa, that last sparked me think up this:
You have 2D slices of 4D objects on your screen. You can only move the laterally. But then they collide and rotate. Your job is to put them together. You won't see the shapes, but the player is required to gain an intuition for what the shape is determined by its rotations and collisions. Of course, you could subtract from the 4D, or add to the 2D . Not really surrealistic though, only confusing.

So you'd want to die as fast as possible per level? That'd be counter intuitive, but it seems a neat twist.

I'd like more simple concepts that cannot be easily replicated in real life. Like tetris. Simple enough idea (make a line and it disappears), but try doing that in real life (real time).

Five Minutes to kill (yourself).