It depends on the type of game for me also, and in general, how much the game and its mechanics are interesting. I've played FFX for about 3-4 hours before giving up on its linearity, but other games have me hooked from minute 1. In general, though, I'll give it 1-2 hours to hook me in.

Some games that I'm on the fence about have demos. If the demo sucks, it has mere seconds to hook me. I'm not kidding. X-Blades turned me off almost instantly. The same for Kane and Lynch and a host of other games that I would have wanted to buy.

As for retail games, if I already bought them, I'm willing to give them an hour. If I don't feel the magic by then, it's going on the shelf. If its a game that I KNOW is going to be epic (like FF13, Heavy Rain or Mass Effect), there's no limit to the amount of time I'm willing to give.

Yeah, I'll try to get back to it, but I'm contemplating going on to the second game to see if that's better.

Depends.
RPG's are the only genre I'd take few hours before dropping (unless it really sucks).

If I pay or get the game for free has a large effect too.

Depends on the game, and prior knowledge. It also varies wildly, as something that I don't like in a game is present early on will shorten this time. I'll usually give anything an hour.

Usually a few hours. I rarely buy bad games though. Jak 2 is absolute ass though and I stopped after a couple hours.

Although Super Mario Kart seems virtually unplayable and I gave up after 20 minutes.

If the game has gotten exceptional praise, I'll give it a while before I realize it just isn't fun.

I dont know , i dont buy many games so i tend to play only those which i really want. But if i dont have any fun in first hour i will put it away, and then get back to it later. Just like i did with Dead Rising Chop Til you Drop

i always finish my games... so i don't give up easily. if a game isn't doing it for it at the time i just change genre and get back to it in the future... in my current collection i have just 3 games to finish... (motorstorm, bioshock and assassins creed) all unfinished because of lack of time and few desire to carry on the "heavy work"

I'll generally give a game 2-3 hours.  If I don't find it compelling by that point, I'll put it down for a couple weeks and give it another try.  If I still don't care for it, then it goes to gamestop.

There's no set time or genre, I just play the game until I get bored.

A lot of times I go back to it months later and finally finish.

Sometimes I just don't go back.