My own gaming preferences don’t tend to run in the absurdist direction, and I’m not sure how mechanically sound a lot of the games that do skew in that direction would be, but here are some things I think are cool that aren’t explicitly meant to be super grim/gritty/horrific:
For oneshots:
Fiasco: I love this thing so much. It’s been described as, essentially, the Coen Brothers RPG. Not very bright people with a driving need for something and poor impulse control, leading to things going catastrophically awry. The actual mechanics are super simple and are mostly used in establishing a framework for the storytelling, and it’s been skinned into all sorts of settings and contexts through what it calls “playsets”, a few of which are included in the base book, a few more of which are in the Companion (which has some interesting things to say about the game but is by no means necessary), and years worth of free monthly playsets are available from their website. Plus fan-made ones elsewhere (in fact, most of the monthly playsets were originally fan-generated, then honored by being officially recognized). I’ve heard it played several times and run it twice myself. It was never less than amazing.
In a Wicked Age: Pulp fantasy roleplaying, extremely rules light. The setting and characters are established by drawing a few randomly selected evocative phrases and extrapolating from there. Characters have a few stats defined entirely by how large the associated die is, (most likely) a “particular strength” that can be whatever the player feels is appropriate, and a pair of “best interests” that they’re working towards. The game essentially revolves around conflicts between the characters in attempts to serve those best interests, and the mechanism there is very elegant. It’s great as a one shot, but can also be strung into a loose series of related stories, like Conan stories were.
For campaigns:
Monsters and Other Childish Things:
Kids have friendly monsters that they can’t let the adults be aware of. I’m not entirely sure what the default antagonists are, but there’s a couple different campaigns/campaign settings for it that have various threats, so really the main thing is kid + monster. It’s built using the One Roll Engine, where you roll X number of d10s for any action and it determines everything it needs to know from how many sets of matching numbers you get, what numbers they are, how many dice are in the set, etc. I think it’s a brilliant system that works very well in games like Wild Talents. Monsters is a little simpler than most of those and by the nature of its subject matter can come up with all sorts of lovely absurd situations (and monsters. I think my favorite was the eldritch teddybear Yog-So-Soft.)
Spirit of the Century:
Other FATE system games might also work, but this one is about turn of the century pulp heroes, so there’s a certain gleeful absurdity built in, as witness the first licensed fiction for it, the Dinocalypse Now! trilogy about invading timetravelling psychic dinosaurs.
Don’t Rest Your Head:
Also from Evil Hat, it’s a game about being so insomniac that you crack open a path into the Mad City, a place where all the nightmares live. It’s a constant balance and struggle against madness and exhaustion, reinforced by mechanics that make you better at solving challenges the closer you get to the edge in both directions…as long as you don’t fall off. It’s essentially a horror game, but it has a sort of surreal, silly edge to it. Puns like the Tacks Man and Paper Boys (made out of newspaper) abound, and suggested madness powers include things like Ninjas! (you are head of all the ninjas in the world).
Nobilis:
Super high concept diceless roleplaying where players are essentially demigods imbued with the essence of some core aspect of reality and charged with its defense and maintenance, competing with various supernal powers, other demigods, and things from beyond Creation bent on the utter destruction of all that is. It’s really very cool, and beautifully, beautifully written. Now, in second edition I probably wouldn’t have brought it up in this context because it came off as this pure, pristine work of high concept stuff that you practically had to be a literature major to pull off. Or maybe theology major. But third edition displays a rather silly sense of humor that you might appreciate. (Also, second edition is long out of print and routinely goes for over $100 online, whereas an electronic version of 3rd edition can be had for like $10). If you’re curious, the author also has a lovely short fiction blog at http://imago.hitherby.com/ . (A favorite of mine.)