Player: Can I do the thing?
Mutants and Masterminds: Yes you can do the thing.
GURPS: Fill out these forms in triplicate.
Dungeons and Dragons: Yes, but it’s really not worth it unless you are a Dream Elf with the Godblooded feat and at least five levels in the Thingomancer Prestige class from Complete Thing. Or you could just play a Wizard, they get The Thing as a 3rd level spell.
Call of Cthulu: You can do the thing, but you REALLY don’t want to.
FATE: That depends, can you bullshit the GM into believing that one of your vaguely-worded aspects supports you doing The thing?
7th Sea: Only if the thing is properly dramatic!
Shadowrun: Yes, but you’ll need a bathtub full of D6s.
Paranoia: The thing is treason.