I am now more than halfway through all available Fringe.
It's pretty much "What if The X Files answered a decent number of the questions it raised?" - The Series.
"Mad scientists did it!" being the main answer, including the "mad scientists From Beyond!" subset. It explains vampires, werewolves, ghosts and the like in the first season alone, like aliens in Doctor Who. Their clearup rate is higher too - if guest stars don't die in the pre-credits they actually stand a fair chance of surviving.
Something like The X Files is a good model for a game - I tried running it once, in fact - but I'd say Fringe is better on balance because of this. The characters more often get to (a) find out what's actually going on, (b) definitely stop it and (c) help people caught up in the episode's threat. It would be a lot less frustrating than an accurate simulation of Mulder and Scully's adventures. Players might let you get away with "you'll never find out..." once or twice in a series, but not once or twice a week.
There are plenty of suitable RPGs, notably investigation games like Gumshoe which already has paranormal and mutant-chasing variants, as well as post-X Files paranormal-hunting games like Conspiracy X, or if you want to go another way model-the-TV-show games like PTA and Smallville. Indeed, I wonder why someone like MWP hasn't licensed Fringe itself.