Back when the first editions of Dungeons and Dragons saw print, the writers had to explain to players from the 70's and 80's that this wasn't a game like Chutes and Ladders that you were trying to "win." In fact, the game could continue indefinitely, with a new adventure for your character in every session.
Having said that, players through the years have tried to achieve their own personal win states for whatever roleplaying game they were in. With that in mind, here are some suggestions for how to win most of the roleplaying games we have personal (or substantial second-hand) experience with!
(These suggestions are not completely serious, but they aren't completely UN-serious, either.)
Babylon 5: Level up enough times that a single PPG shot won't kill you.
Call of Cthulhu: Don't die or go insane this session.
D&D / AD&D 1.0: Figure out how the heck to play Dungeons and Dragons.
D&D / AD&D 2.0: Cause your DM to pull their hair out, burn all their RPG books, and join a convent. Alternately, if you're the DM: Kill all the players. Not the characters, the players.
D&D 3.0 / 3.5: Get to level 6, so you can finally go into a "prestige" class and play the character you wanted to.
D&D 4.0: Win or survive every combat encounter, until you best the final boss fight and beat the game at level 30.
D&D 5.0: Survive D&D 2.0 dungeons, using a D&D 4.0 character, until you acquire one magic item from the D&D 3.5 rulebooks. (This may take several years.)
D20 Modern: Get to level 4, so you can finally go into an "advanced" class and play the character you wanted to.
FATE Core: Insert your own win condition here (then invoke it as an Aspect during play).
Pathfinder: Convince the GM to let you play the character you want to play.
Pathfinder Society: Buy enough Pathfinder stuff, and kiss up to enough Venture-Captains, to get the boon (and the books) that you need to start over from level 1 as the character you actually wanted to play to begin with.
Traveler: Don't die during character creation.
Special bonus for those who've been subject to it
FATAL: Cast FATAL.*
* Although really, the only way to win is not to play.