The Paranoia role-playing game is probably the longest running satirical role-playing game available in print. A recent successful Kickstarter project funded the new edition hitting the shelves currently. The game is published by Mongoose Publishing and project managed by seminal designer James Wallis. What should make a lot of people happy is that the game is a compact, streamlined take on the classic game that comes in a boxed set that includes the game and dice. Probably my favorite bit of the new game is that the character "sheets" that you can get for the game are in fact dry erase mini-boards, in keeping with the lethality of the game.
The rest of the Paranoia Red Clearance Edition design team are Grant Howitt (probably best known for his work on the Unbound RPG) and Paul Dean (one of the parties responsible for the Shut Up & Sit Down site, as well as work on video games).
I'm not sure that another design team could have produced a game that manages to capture the paranoia of Paranoia quite as effectively for the contemporary gamer. The game is equally funny, poignant and scary, in that way that novels like Brave New World and 1984 can alternate between humor and terror. The idea of the Alpha Complex and The Computer, and the eternally red-shirted Troubleshooters, should be a scary one, but it is made palatable to us through the humor of the game, as the sometimes uncomfortable laughter sometimes cracks the uncomfortable feelings.
The game can be challenging and heady stuff, if you so want it to be, or you can play the game on the surface and embrace the simple humor and more escapist, "shoot 'em up" qualities of the game. Spoiler Alert: It plays excellently either way.
I have a long history with the Paranoia game. I ran the classic edition at a gaming convention, back in the 90s, when I lived in Cleveland, providing my first encounter with the setting and the system. Some friends ran the gaming HQ for the con, and approached me to run some "non TSR" games for the convention, and Paranoia was among them. I hadn't actually played (or ran) the game at this point, but one of the HQ people told me that it wouldn't really matter, and most of the people in the event probably wouldn't have played the game either. The adventure was RPGA sanctioned (back in the days when the RPGA sanctioned events that weren't published by TSR) that had Troubleshooters that were plays on the classic Silver Age incarnation of the Justice League of America. There was a giant drilling machine. Hijinks ensued and the table had a bunch of fun.
Unfortunately, I didn't get to play the game a lot in the years since that convention. Like with any game that uses humor as a tool, you really have to have the right group of people playing Paranoia, or things can get out of hand quickly. On top of that, satire can be a form of humor that is particularly difficult to bring across. For a successful and effective game of Paranoia you really need to have the gaming group on point and agreeing to the satirical elements. Otherwise, like with so many attempts at humor in gaming groups, things degenerate to slapstick and Monty Python jokes.
If you've never played Paranoia before, the high concept is pretty simple. The world of the Alpha Complex is believed to be a post-apocalyptic world of the far future. Of course, it could be a hidden society, ala an M. Night Shyamalan movie reveal. The Computer knows everything, and is efficiently running the world of the Alpha Complex. Except for when the story requires otherwise. The Troubleshooters are highly trained and competent agents of The Computer, given the best training and upgrades to their systems that will allow them to work in the best interest of The Computer and for the safety of Alpha Complex and its inhabitants. Except for those times where they are incompetent and haven't been completely filled in on what is going on around them. Not to mention the fact that they are members of some secret society that has goals that run contrary to those of The Computer. It is a complex game with a lot of moving parts to keep in mind while running, or playing, it.
You don't have to be concerned with all of these things all of the time, but it is important to remember that Paranoia can be a lot more complex than it seems. A lot of the humor of the game comes from encountering the dichotomy of the realities of the world of Paranoia versus the reality as presented by The Computer. The Computer would never lie, would it? There must be other reasons why things aren't working the way that they are supposed to work.
Characters have an attribute called Moxie that keeps track of their stability and calm. You can use them to add dice to a roll, re-roll a dice roll or activate a mutant power (mutant powers are very serious, and should be reported and registered so that The Computer fully understands the capabilities of Troubleshooters). However, at zero, your character suffers a "break" from reality, due to the stress of Alpha Complex and being a Troubleshooter. "Losing it" can mean that the character is extremely happy, feels disconnected from themself and their actions, extremely angry or hateful or they have an overwhelming desire to act in way that is different than normal for them. Moxie isn't unlike mechanics like Sanity in Call of Cthulhu, but it is one of the tools for helping to create the feel of the world of Paranoia. It is a mechanical way to address the differences between the stated realities of the game's setting and the actual realities of it, as encountered by the Troubleshooters. Characters have been indoctrinated since "birth" in how the Alpha Complex and The Computer works, and encountering that these truths aren't as true as they think that they are can be extremely dangerous to the psyches of characters.
It is also important to know that your Paranoia characters aren't just a single character. Instead, they are a series of clones created by the machinery of the Alpha Complex, overseen by The Computer. The lethality of the game is very real. It isn't unusual for a game to have multiple Troubleshooter deaths within the first few minutes of play. When one clone is killed off in the service of The Computer, another is decanted so that the mission can continue. Sometimes these clones aren't as up-to-date as the clone they are replacing, so there can be gaps in memories and experiences.
Each character also has a Cerebral Coretech which is usable for a number of things. It can calm or stimulate a Troubleshooter in times of need. It can assist in communication and relay information from The Computer that Troubleshooters might need to complete their mission. It serves as a black box that can record missions, and report treasonous activities. The Cerebral Coretech can also provide "upgrades" that allow the Troubleshooter a better chance at success on missions. All of these functions work as well as everything else in the Alpha Complex.
Equipment and mutant powers for characters are tracked via the provided cards for characters. In addition, Action Cards are used by players to tell what their characters are going to do during a particular combat action. If you are out of Action Cards, your character cannot act during a particular round. There is also a Computer Dice that you roll during tasks to simulate the unpredictability of the Alpha Complex and The Computer. Despite its name, there is only one Computer Dice. The designers figured that "die" was used enough in the game and might be confusing if applied in this regard.
I think that Paranoia is the poster child for the "not all games are for everyone" sensibility. Not everyone wants to play humorous games, particularly those of a dark, satirical bent, and Paranoia embraces that humor. If this isn't for you, then Paranoia probably isn't for you. While Paranoia can be played as an "escapist" shoot-em-up game, you will lose a lot of the bit of the game's world if you play it in this way. I also think that Paranoia is best suited for short series play, where you play the game for a few sessions and then move on to something else (even another game of Paranoia). It really isn't a "let's play for a long time and develop the personality of these characters" type of game. Paranoia is a role-playing intensive type of game, but when death can lead to a new clone with a faulty memory or poorly formed personality, it is hard to maintain a continuity of character with the game. The setting of the Alpha Complex is also malleable and subject to change as the characters explore their world.
With the right group, Paranoia can really sing in play. Embrace the inconsistencies and dangers of the game's world and dive right into things. I think that there is a small list of games that all gamers should give a try, at least once, to be able to experience differences in playstyles, presentations of setting and how rules can impact play. Paranoia is one of the games on that list. By usurping some of the paradigms of play in role-playing games you can learn a lot about what you like, and don't like, about play. Without challenging those assumptions you don't really learn why something works for you, and why other things do not. It is also good to directly learn how other games work, rather than just assuming based on what other people tell you that a game is and does.