As a GM, I have a standard house rule that the players can invoke on any occasion (if I agree at the time). It goes something like this:
If you're in a really bad situation, you're going to die etc. Ask for a luck roll.
If you can think of something funny but near impossible. Ask for a luck roll.
Most of the time, if the players asked for a luck roll, I'd give it to them, they roll a 20 sided dice, if they get a 20 (modified only by rabits' foots, four leafed clovers etc), they are very lucky, and/or succeed/don't die etc.
Here's some examples, from one particular player (Daniel Hopkinson aka Hoppy) who can ALWAYS roll a 20 when he really needs it (even on MY dice):
VILLAGER TO HOPPY: "If you're the god of Justice, the... WHO STOLE
MY SHEEP?!"
HOPPY: "err... Him" (points)
-Hoppy gets a natural 20
HOPPY TO GM: "If I can't shoot him, him being a player character
and all, can a satellite deorbit onto his head?"
GM: "Only on a natural 20"
-The death of an absent Player Character.
HOPPY TO GM: "It was a twenty"
GM TO HOPPY: "It was a three, GM reserves the right to modify dice
rolls"
-GM getting sick of Hoppy's twenties
PHIL (another player) TO ANYBODY: "If Hoppy can roll a 20, then
so can I"
-Phil failing.