The player characters all have amnesia (not the interesting part).
They have no idea who they are or what they can do. Each time they
try to do anything for the first time they make two rolls with a die,
any die on hand (good for when you want to play but only have a D6
around). The first roll is what their skill will be for that task from
then on. The second roll is the attempt to accomplish the task. Roll
under the skill to be successful in the task.
The system is not sustainable because after an hour the character
sheet is filled up with skills and it is hard to find "read a
wristwatch" on the page. But it is fun when you don't have time or
supplies for a more in-depth game. It is also best for "normal human"
characters because who wants to sit for an hour and GM a guy "trying
to shoot energy from his eyes" (although if you get too bored there
are creative solutions for trying to "fly"). And "normal human"
should also assume that the characters have average capabilities, a
"walking" skill might be funny at first but a character who has a 1
for walking might not be that fun to play.
In this, everything is a skill - even common attributes. So, "lifting
heavy things" might be part of what is usually Strength. "Jumping over
something" might be part of Dexterity. The important part is the
skills should be generic enough to be used more than once but not so
generic they are used constantly - the balance between the two makes
the discovery of each new thing fun.
No hit points, the GM should provide negative consequences for
actions. Remember that just as "punching" is a skill, so is "taking a
punch" - you might be like Mike Tyson but have a glass jaw.
The point is, this is a quick way to play a fast one shot game that
might give you ideas for other characters to play.
This idea came from a friend of mine when we played a quick game set
as elementary school kids, we used D4s and had stats like "dental
hygiene" and "parental coolness". My Character had high dental
hygiene and very uncool parents...