When I was a kid, there were some games which i'd get stuck on and never be able to pass in order to beat the game. Though, this probably is due to the fact that I was young and not as able as I am today. Some of you mentioned the missions in GTA: San Andreas but I can't attest to this due because I don't think I got far enough to do so. I remember the mission in GTA: Vice City where you had to race Hilary the Lawyer starting and ending outside of the Malibu Club, that mission took me many tries and bouts of frustration before I completed it. The later missions of GTA III were also frustrating, the ones involving Catalina, the Yakuza, etc. The one that I got stuck on involved crashing into and destroying the expresso stands...I tried and tried but with no luck.
Oh and I became stuck at Braska's Final Aeon at the end of FFX, but this could be due to me being underleveled (I am almost always underleveled when I play RPGs, hardly taking out time to grind and level up although im starting to break this habit due to not wanting to be STUCK at any point in time.) Aside from these, I cant recall any games which made me throw in the towel because I was absolutely stuck at a point. I don't always complete the games I start, but this is mostly because I have no motivation to due so and not because I have actually been beaten by the game.
I couldn't beat a level in Halo 2 where you're fighting a ton of these gorilla alien dudes, if only because my friend insisted on playing on hard difficulty. I am not very good at FPS! If any games really and truly beat me at skill, it's FPS games.
The brutes? And yeah Halo and Halo 2 are brutal on their legendary modes. It took me a while of learning the map layouts and planning a strategy with what little ammo there was to work with in order to finally beat the legendary modes. Though Halo 3's campaign, as Brown pointed out, is vastly(okay not really) easier than the previous two installations. I'd say that Halo 3's legendary is equivalent in difficulty to your average H2 level on Heroic. Oh and I always had more trouble with H2's legendary mode than Halo's, probably because the amount of aim assistance also applied to the covenant forces as well as character that the player used.