I know there are tabletop games deliberately designed to be funny but I've always found those fall a little flat when you actually try to play them. They may be a lot of fun to read, but they never seem to play quite the same way. The ones that come to mind are Toon and Paranoia and I've seen people have fun with them but I wouldn't say they hit any higher than a good session with more traditional games. I will say that superhero games have a lot of potential for humor. From ridiculous concepts to the things players try to do during a game, the scope is wide open. That said I've seen whole groups paralyzed by funny just playing regular old D&D.
In the interests of putting the word out on a lesser-known game here's one I've run twice and had a lot of laughs both times:
Yes it came in a magazine and I think you can tell from the cover above just what the game is about. I can't explain the premise of the game any better than it does itself so here it is:
The central conceit is that each character is an armored trooper with a tough and extremely capable suit of powered armor but the documentation is almost non-existent and repairs are varying in quality. This means each character has somewhat different capabilities than the others in the party. Your skills are basically things you have figured out how to do consistently with your suit. Here's a character sheet:
That list of "EE Suit Functions" is pretty much your skill list but it is expandable. Everyone starts with 5 skills. Task resolution uses a simple table that's right there on the sheet. You can try to perform functions you don't have but the difficulty bumps up two levels.
The suit also functions as the equipment list as they can do pretty much
anything. From the rules: "Most functions remain unlearned by most
troopers and a suit will frequently surprise its user." Also "... humans
are and will remain lazy - just learning enough to get by, or more
importantly learning only what they consider interesting." Part of the fun of the game is figuring out new ways to use the suit to make things happen.
There are 4 races available that add some capabilities, mainly appearance, damage levels (see character sheet above) and different chances of getting one or more of the five "Traits". Since you're in an armored battlesuit there are no traditional stats like strength. Instead a character might be Durable, Fierce, Imperial, Inventive, or Spirited. This is determined randomly. One race is also Empathic and might have some Funky Powers available as well. Some skills are only available to characters with a particular trait.
There is a complete and fairly interesting character advancement system in here as well, complete with titles:
First, a character chooses to enter the game as one of the four beginning titles listed at the top of the page. Up on the character sheet you will see a list of nine categories of "deeds". A character has to achieve one of each of these to advance a level. When they do they can choose any same or higher level title that is connected to their current title. The "Ignobles" are purposefully left loose though there is a description of each and some examples of how they might be achieved. It's an interesting concept that I would like to use more.
All of this is contained in 40 pages of rules, setting, and examples. It's fairly dense text with sidebars and callouts that is a great example of how to distill a game down to its essence. There is also a 13 page adventure involving a mission to retrieve a universal translator. Its a real, complete adventure spread over several locations, with multiple scenes, complete with maps and diagrams.
OK, so where is the funny? Once players get into the spirit of the game and the loose/light nature of the rules, they start trying things, and those things are often pretty funny. Given the flexibility of the suit, and the likelihood they will not die from a single mistake or bad roll (the hero point mechanic here is "make-rolls" because spending one means you automatically made the roll) and they loosen up and start having fun. Trying to adapt their limited, yet broad capabilities like "hydraulic press" or "vacuum pump" into something useful leads to call kinds of interesting scenarios.
The included adventure helps too as it quickly turns into a Hitchiker's Guide-esque run of dealing with things like a ridiculous bureaucracy, a talking ships computer, used-spaceship salesmen, police robots, and some more traditional space stuff like hijackers, gas giants, and navigational difficulties. If the DM and the players are feeling it then the whole thing can be pretty funny. There were a few other adventures published in the magazine after this issue and I recall them being funny too but this one is a great example of what is possible.
I remember these as a couple of my funniest sessions so I'm calling it a funny game. If you want to talk funny sessions I have had quite a few in other games but this particular game seemed to bring it out pretty nicely.
UPDATE:
The current website for this version of Space Gamer is
here.
Some background on the setting is
here.
A primer on the rules (they use them in multiple settings) is
here.
The site looks pretty old but the forums are still somewhat active. I'm not going to join it (paywall) but if anyone does let me know how it is.