Weird, you say? Fringe?
Apocalypse World - First game to use the Apocalypse Engine. Your character progression is tied into your role. Fighty types get fighty skills, weirdo psychics get to talk to the End of the World, and leaders actually develop the settlement as XP spends.
The Morrow Project - 150 years after a nuclear exchange, you awaken from cryogenic suspension to discover that someone sabotaged the project and the central base is gone, leaving you alone to try to rebuild, or just survive.
Alma Mater - High school. Just High School(you know, drugs, sex, etc.) Art by Erol Otus.
Stalking the Night Fantastic - Weird is this game's first and middle name, followed by Awesome. You're deniable government assets trying to prune down the supernatural Bad Stuff and protect the citizenry and Good Stuff. Remember, there is nothing you can investigate at midnight you can't investigate twice as safely at high noon.
Justifiers - Furries. In. Spaaaace! Also, a thrown rock is more deadly than a laser gun.
Macho Women With Guns - It's.. pretty much what it sounds like. It's a parody game, and meta-parody at that -- there are rules systems in it making fun of other, famously clunky rules systems.
Dogs in the Vineyard - Religious Police in alternate-world Deseret, 1800s.
It Came From The Late Late Late Show - You play actors on a completely improv, shoestring production of some UHF(ask your parents) station's fantasy/sci-fi/horror show.
The Drones - The game of single London men in the 1920's social clubbing. Get out your flat caps and starter handles, or you'll never make it to the boat races in time to stop Neville's brother from getting married and leaving the club.
Atomic Robo - The FATE system isn't exactly fringe, but Atomic Robo is weird. And Awesome. And has a SCIENCE phase cooked into the rules. And has Jenkins, the Flying She-Devils of the Pacific, and Doctor Dinosaur.
Judge Dredd - The Judge Dredd RPG. Weird is where it starts. Chasing down a Blob gang growing black market dinosaurs for the rogue droid's illegal dino-fighting ring so they can steal the audience from the fatties beliwheel triathlon. Or, you know, Wednesday.
That's the stuff I have within easy reach.
..I may have a problem.
ALL HAIL KING TORG.