Platformer: 15 minutes; If the controls or physics feel wrong, I stop playing.
JRPG: 45 minutes to an hour; if the battle system isn't awesome, I'll stop playing
RTS: 2 hours to 50 hours; If the learning curve takes more than a week, I stop playing.
Action Adventure: an hour; If the combat or the exploration gets dull, I stop playing.
FPS/TPS: 30 minutes to an hour
Mini game compilations: 10 to 15 minutes; If it's not to the point by then, I stop playing.
Sports games: 10 to 20 minutes; If it doesn't feel right, I stop playing.
Fighting games: 5 hours; If I can't make much progress after that, I stop playing.
Racing Games: 2 to 3 hours; If I can't get a feel for the physics or controls, I stop playing.
Beat'em Up: 10 minutes; If the combat's not fluid, I stop playing.
These are usual cases, it varies more depending on the game.