Good thread.
Personally I tend to check walkthroughs or google to a forum where someone else has had the same problem quite a bit these days when I'm stuck.
As a general rule I do try to figure stuff out but it depends a bit on what type of situation it is. If it's just a case of, I'm fighting a really tough boss and keep dying, I will likely persist for a long time before seeking advice. If it's something along the lines of not knowing where to go then I am much more likely to check a guide sooner rather than later as often there is no 'skill' involved in that. In particular visual/video walkthroughs can help here, often it will be something stupid like not realising there was a doorway somewhere, or that you can move through a grate.
Things like secret areas or collectibles I never look up.
edit: One thing I really, REALLY hate is when games have a misleading puzzle. You know, where there's more than one potential solution but only one of them actually works. Case in point would be in HL2:Ep2 where you have to put grenades under a ramp to catapault you up to a ledge. There was a box of grenades nearby, and a little space underneath the ramp. OK, so I'm not a total retard, I can figure that out. Chuck grenade in the space, it will explode, and move the ramp. It does. Problem being, the ramp is now acting like, well.... a ramp. It's pointing up at the ledge and almost reaches. So it gives the impression that you are supposed to actually use the ramp as y'know, a ramp. Queue endless attempts at doing sprints up the ramp followed by crouch-jumps etc that really felt like they should be getting me to the ledge if it wasn't for some kind of ****ING INVISIBLE WALL.
Sigh. Actually pretty out of character for the HL2 games as normally the puzzles don't need to to execute your moves exactly as the develop intended, you get a bit of leeway.