THE DUMBEST GAME I EVER HAD THE MOST FUN WITH:
Tales of the Floating Vagabond (Avalon Hill)
Sometimes good mindless fun is just the thing to brighten up a long mentally taxing day.
That's why Harry always plays a Barbarian.
As for Dumb & Fun RPGs I would have to mention
Paranoia. Where the directives are; The computer is your friend, do whatever it tells you and kill the commie mutant traitors (your all commie mutant traitors). You have at least 10 clones of yourself, waiting to be dispatched to near your location after friend computer acknowledges your bodies demise. All the equipment is color coded, and it is illegal to use equipment of a superior color, just because it is better.
Toon, where you play a cartoon character in a Looney Tunes Adventure. Where you can break the laws of physics by failing a smarts roll. Your character never dies he just falls down for 3 minutes real time. Reads like a bastard child between GURPS, Tales of the Floating Vagabond, and the Saturday morning cartoons of the 1980s.
Khaotic Aliens from another dimension are invading earth. They're slowly winning. The governments have found a way to go to the aliens home dimension and fight them there.
It is found that psychics can use this earth & alien tech machine that some mad scientist invented to posses the body of one of the aliens. Trouble is unless the entire party is using the same machine they could be spread across the entire alien world regardless of how close together they are in this one. To complicate matters, everyone who uses the same machine posses one alien body. To top things off everybody on the team has an secret agenda that most likely does not completely with the primary mission or the secret mission of anyone else on the team.
In a sense you play an alien with multiple personality disorder who's goal it is to allow creatures in another dimension that he might not even know about to profit from the his worlds knowledge. Because the game makes those not in control of the body incredibly powerful psychics, it still allows people who aren't driving to do stuff. However, the entire game session can quickly devolve into players bartering with each other to achieve their goals while denying others theirs. At which power runs out on the mad scientists machine that brought them there and they all return to earth, with everyone failing their missions.
Schizophrenic role playing at its craziest.
For non-RPGs I could go with: Kill Doctor Lucky; Munchkin; and Beer, the card game, by Stupendous games.