Paranoia. basic idea is, everyone is a clone that works for 'friend computer' that controls the entire place. you do what the computer says, or it kills you. the computer is also super paranoid and assumes everyone wants to destroy it.

Darwin's World, Dark Heresy, Eclipse Phase, the actual Fallout RPG, etc.

Alright. Thanks for the suggestions.

looke up traveller, me and my friends are playing that and it's a hoot

Paranoia is not really a beginner's game. Fun certainly, and you don't have to invent your setting, but gameplay is intentionally very different from your standard RPG.

Darwin's World I don't know. sorry. Apparently it is supposed to be D&D postapoc?

Dark Heresy is one of three RPGs in the Warhammer 40k universe which differ largely in character power level. Presumably the other two would also be okay if you are familiar with that setting.

Eclipse Phase is post-singularity, where much of the population does not have bodies, and many that do are no longer human. Evil AI controlled by aliens broke Earth, so we live in the rest of the solar system.

If you don't know what Fallout is, you just haven't been paying attention.

Traveler is often jokingly refereed to as the game where you can die during character creation. There are lots of charts. It is built for high space travel adventure, but you can turn it into anything else just by staying on a certain planet.

I am also shocked that Shadowrun has not been mentioned. It is the quintessential cyberpunk game. Evil corporations, cybernetic enhancements, magic, and computer hackers.