Paranoia is a simple game at concept. Other RPG's you work together as a team to overcome huge obstacles, basking in the knowledge that your heroes made the world a better place (usually).
In Paranoia, you live in Alpha Complex, one clone in a pack of six. Recently promoted to Red Clearance for exposing a superior as a traitor-commie-mutant-spy. You work as a troubleshooter. Your job is to find trouble, and shoot it. Alpha Complex is run by your friend, computer. The computer wants all citizens of Alpha Complex to be happy and productive. But at the same time Computer is insane, and completely illogical. False data is everywhere. Superiors are constantly sabotaging the work of underlings (and overlings), In an attempt to get ahead.
You sabotage others by exposing the faults, or arranging little accidents, or taking justice into your own hands. Traitors are members of secret societies, or mutants.
Bad news, you belong to a secret society, also you are a mutant.
You might be thinking, "at least I have my party of teammates!", with a sense of optimism. You might be thinking you can band together to destroy traitors, or even Computer. But here's where Paranoia is set apart from the rest. You can't trust anyone. ESPECIALLY your teammates. Because things are going to go wrong, that point is unavoidable, someone has to take the blame, and you sure as heck don't want it to be you.
The gameplay usually involves a mission briefing, R&D providing untested/dangerous/sometimes broken weapons for field testing, an impossible mission, NPC's/Players undermining everyone involved, placing the blame accordingly, and killing each other when someone starts acting a little too shifty.
If you run out of clones, you can create a new character and continue where you left off, with a couple small changes to your mutant powers/secret society. The game ends when you either complete your mission and receive a briefing from the computer. The game is fun, action packed, and comedy ensues. I highly recommend this game.