Hmmm, big question here.
One system that I have used successfully for many different settings, one that is easy for even non-roleplayers to pick up on, is
Over the Edge. Similar to FUDGE and
Spirit of the Century it is a "build your own idea" -- you decide on a Central Trait, two Side Traits, and a Flaw. Very broad, very intuitive, but it does require a certain amount of GM-player input and interaction to get it to run smoothly. Still, it is a game that I can get up and running within an hour, that the players grasp, and that a wide variety of people enjoy.
On a more detailed level, I really like the HarnMaster system; in fact, it is probably the only straight-percentile system that I still like. If you roll under your percentage, you succeed; if you roll over it, you fail. If the roll ends in a 0 or a 5, you have a special success/failure. Character creation has options for purely by chance, utterly by choice, or a mix-and-match method -- I prefer this latter. Again, I have been able to move this to system to multiple settings.
The revised
World of Darkness system works pretty neatly. It is a dice pool system where the dice pools don't get out of hand. If you roll 8 or better, you have a success; if you roll less, you have a failure. You count the number of successes to determine who is ahead or whether you have completed a task. This is also a great system for introducing new gamers -- it is simple, obvious, and intuitive. Of course there can be a fair amount of interpretation with the interactions between certain powers, but that is a comparatively simple matter as long as the players and GM get along well.
Ars Magica is good, but basically it works best as a fantasy/magic system. I haven't really been able to port it over to something else, but it might work. It is rather more difficult to explain to non-gamers, or even gamers who are only comfortable with a single system (a very large percentage of gamers in general).
In the end, I prefer games that are cooperative over competitive.
