I hated Resistance after the first mission, then all of a sudden the game got good.

You said you gave up on Okami after three hours, even though it's a 40 hour game. I'll criticize you as I see fit.

about a week, then i suddenly think, this shit is boring me, and trade it in the next day

Well once I quit I popped in HotD:Overkill and had 6 hours of pure fun.

I gave up on Half-Life before the game even began (about 1/2 hour until the resonance cascade). Next year when I gave it another try I felt it was the best game ever.

It really depends on my mood as to how long I give it to draw me in.

I can only speak for myself, but I can't think of a single time between NES and now when I have played a game for more than an hour without liking it only to have it suddenly become an awesome game.  I've trudged through a huge number of games that I wasn't particularly enjoying, and not once in my life was it ever worth doing.  Now, I'll give a game maybe 2 hours and if I don't enjoy it, done.  The closest examples are Mass Effect and Fallout 3, two games I really wanted to like because of my Bioware love and my love of previous Fallout titles.  I played both for a while, and wasn't enjoying either, but figured I'd give them the benefit of the doubt.  Well, neither game improved and I wasted a lot of time playing games that I didn't like.  Just ecause you thought Okami was fun doesn't mean that someone who hated the first 3 hours was going to like the next 37.  In fact, it is pretty likely that if you don't like a game it's never going to grow on you, because the process of playing it while not having fun just makes you hate the game more.

And before you say anything, I thought Mass Effect had an awesome story and thoroughly enjoyed seeing it develop when someone else was playing, but the gameplay made me want to commit suicide.

Usually it's the first bits of information and pictures... And that's both, not only one of them (well, I do have some sort of an opinion basing on either). If that's not enough, a maximum of an hour ought to do it, though it may not convince me completely (sometimes it's just hard to believe the game is bad and I expect it to get better).

Which reminds me that I should really trust my instincts a lot more before trying out new games.

Depends on the genre. I'm currently playing Tales of Vesperia and it finally got interesting about 15 hours into it. I give RPGs longer timeframes to entertain me.

I put in about 25 hrs in Blue Dragon before I came to the conclusion it wasn't going to get any better and stopped playing it.

Devil May Cry 4 I gave 3 levels and were bored with all 3 and never played it again.

This is like me with MGS 2. I played the game for about 7 hours and then I began to like it, it grew on me. And now it's my favorite series, patience brings good things.

It depends sometimes within the first 10 to 20 minutes it took me about 3 or 4 hours of farcry 2 to realize i hated it. I cant stand games where every mission is as far as possible from your location for no other reason than the mission is dumb and easy and its more of a pain in the butt getting there than to do it. 30 minutes travel time there 5 minutes to do the mission and 30 minutes back i hate that.