Simple three-player game. Each player secretly picks a number from one to three, then all are revealed at the same time. Each player who picked a number that nobody else picked gains that many points. Everyone else gets nothing. First to 7 points wins. Would probably work with 4 players too.
Thinking about a modular roguelike that is expanded by people playing it, which isn't new by any means. Maybe some kind of "deck-building" game where you're a summoner building up a synnergistic horde of minions from prefixes, suffixes and modifiers that you gain as you progress through the dungeon. If you reach the end of the game, then your "deck" becomes a blueprint for a dungeon floor. ie: come up with a good ice "deck" and maybe the next player will have to travel through an ice level populated with those monsters.
Or maybe the visuals are the customisable part? Make a card game ala magic that starts out with all the cards blank, but players get to draw their own art as they play, slowly collaboratively illustrating the game. After playing a round you're presented with 3 different illustrations for the same card and you vote for your favourite. The exact voting mechanism will be a bitch to design, but it's one hell of a gimmick that is sure to garner public attention from game sites.
Inspired by Star Guard, a 2d scrolling shooter where you die in one hit but have infinite lives. A meatgrinder of a war where wave after wave of disposable soldiers with increasingly outrageous prototype guns are sent to the front lines in desperation. Each life is a new soldier and carries a new experimental gun. You are given brief uninformative instructions on your weapon when you spawn. Some will be useless in the situation where you are, others will be overpowered, others will be suicidal. Short bursts of discovery and fun, where every failure is a new opportunity. Grenades that bounce unpredictably. A fantastic plasma gun that kills you if it overheats. A super-rocket that only has one shot, leaving you unarmed afterwards. A boomerang gun whose shots you DO NOT want to catch. A nuclear grenade launcher whose blast radius is greater than its maximum range. All mixed in with varied but more mundane weapons.