Paranoia was first released, appropriately enough in 1984. Set in a sealed habitat called Alpha Complex sometime in the future after a nuclear war has destroyed human civilization, the game centers on the missions of "troubleshooters" working on behalf of The Computer, an artificially intelligent machine that acts as lord and God of Alpha Complex, both maintaining it and protecting against enemies internal and external. Paranoia's central joke -- the game is, after all, a broad satire of the Cold War and then-contemporary culture -- is that The Computer is insane, having ordered human society within Alpha Complex into something humorously inhuman and who sees imaginary enemies everywhere, most especially from secret societies (such as "Commies") and mutants. Naturally, all player characters are both mutants and members of secret societies as well as troubleshooters, fostering an atmosphere of madcap secrecy and dissimulation that plays nicely into the game's central premise.
Consequently, the missions on which the characters are sent by The Computer are often absurd, based on false premises and riddled with untruths, half-truths, and outright falsehoods, because the society of Alpha Complex largely functions by lies agreed upon. Thus, characters, as well as NPCs, must continue to say and do the "right" things, even when they know that those things are mistaken or incorrect, because, to do otherwise runs the risk of one's being denounced as a traitor and executed. And while Paranoia provides each character with six clones, thereby making it easy, both rules-wise and in the game's setting, to replace a dead character, self-preservation is nevertheless a prime motivation for many, if not most, characters, especially if it can be achieved at the expense of another character's own quest for the same.
It's here, I think, where a large fault line in Paranoia lies. Paranoia is an unambiguously "confrontational" game. Or perhaps it might be better better to call it "competitive." Regardless of the term used, the GM most definitely is out to get the player characters and player characters can advance by backstabbing their fellows. Now, those of who enjoyed Paranoia recognized this dynamic as all part of the fun and, given that Greg Costikyan was one the game's designers (along with Dan Gelber, Ken Rolston, and Eric Goldberg), I think it's safe to bet that this dynamic was intended, at least in part, as a commentary on the way many roleplayers enjoyed their hobby. However, not all gamers, then or now, find Paranoia's explicit encouragement of slapstick-riddled betrayal to be enjoyable. Indeed, I've known several roleplayers who considered Paranoia to represent everything they hate about the hobby and their fellow gamers.
Now, I've always had a soft spot for Paranoia, in part because it plays to my strengths as a referee. I'm good at creating quirky, possibly insane NPCs and portraying them in an amusing, if slightly sinister, fashion. Likewise, I have little difficulty switching between Three Stooges-esque hijinks and black humor, both of which are, in my opinion, essential to a good Paranoia game. Note that I didn't say "campaign." While there are rules in the game for improving one's character over many adventures, I can't recall ever using them. Likewise, though I've played the game many times over the last 25 years, I've never run anything more elaborate than extended one-shots with it. I'm not sure that Paranoia could be played over the course of many adventures, except in very special circumstances. Instead, like many humorous RPGs, I enjoy it most as a change of pace, a "palette cleanser" to be played between longer campaigns of a more "serious" sort.
Which reminds me: a note on "seriousness" seems in order here. Paranoia is a humorous game. On the face of it, you're not supposed to take any of it seriously and I think that attempts to play the game straight bleed some of the joy out of the game. At the same time, I don't think there's any question that, like all satires, its designers meant for its critiques and commentary to elicit thought and examination about the real world. The jokes here aren't all just pratfalls and Warner Brothers-style lunacy; they're intended to serve a purpose.
In my opinion, it's here, rather than in all the player vs. player and players vs. GM silliness, that Paranoia's biggest fault line lies. Many gamers -- and rightfully so -- don't want a RPG to be used a platform for political discussion (or diatribes), however thoughtful or amusingly presented. In the hands of an unskilled referee or one with a transparent agenda, I suspect Paranoia could prove a very unenjoyable experience for many players and that's the game's real Achilles heel. However, to eliminate the political/social satire would similarly drain away the much of the zany genius that makes the game so appealing to those of us who love it. It's a fine line, one that many referees simply cannot discern, making a good Paranoia adventure difficult to pull off. But in the hands of the right referee, it can be a thing of beauty.