If I have nothing else to do, I keep trying. If I have no solution, I look up a solution and keep trying.
In Pokemon Ranger, a unique thing happens that only happens with some games: My hands become completely numb and I have to wait atleast one or two days to continue, esp. since I'm using my finger on a touchpad instead of a stylus.
I might also switch to another character/arc/level, if such a thing is available (like in Sonic Rush), or a similar game in order to get experience. I remember I did that alot when I had a GBA, since most games played the same way. Sonic Advance helped me complete a Megaman game which in turn helped me complete a SpongeBob game, etc. I've done the same thing with online games, using RS to help me with S4 League which helped me with CoH:GR, which then helped me with Vindi - which helped me with TERA...
Yeah, so I normally either "try", "get help", or "switch". Though I never cheat since that would ruin the challenge. As in, I use walkthroughs but no hacks.
It depends on how long I've been playing most of the time, and whether or not what's killed me is actually beatable at my current level. If I just messed up, I'll usually give it a second try, but with something like a JRPG I'll usually put it down and come back to it later, when I'm ready to invest some time grinding.
The last time I saved, or how much I have to do again, factors into it as well. If I have to do a whole level again, I usually just quit, sometimes for a few days. I hate repeating myself, just to lose again at exactly the same point.
When I play a game for the first time and lose, I'll give it another try. If I lose again, then I may try to beat it for a third time. If I still lose, then I will simply pull out the game from my console and put in another. I might play the game again at some point, but I'll play it only when I have enough motivation. xD If I don't feel motivated, then I will most likely end up not touching the game ever again.
It honestly depends how much time I have. Sometimes when I'm playing a game I have all the time in the world, but other times I'm playing and don't have that much time because I must go to work or am going to hang out with some friends or something. Normally though, I'll keep retrying until I beat the checkpoint.