My tastes in gaming has changed over the years. I think that when I was a kid, I would play anything. Nowadays it really comes down to mechanics. I try many games but if there is something with the controls or the design of the game that I do not like, then I will stop immediately. I'm not worried about having wasted time or money, as I already know I can't play all of the games I own.
So it could be right away, or it could be after an hour or so, it really depends on the game.