Ugh, happened to me the other day playing Mortal Kombat online. The guy kept turtling on me, which is annoying because my character doesn't have any moves that can get in on him. Plus my style is more defensive, trying to zone the guy until he makes a mistake and then I unleash combos on him. What sucks the most is that he just kept chipping away at my health, then any time I got near, he just teleported away. It's kind of lame that that can happen.
And while this isn't necessarily a video game moment itself, but I hate it when my opponent in Starcraft 2 is bad mannered. The worst is offensively GG-ing you. That is incredibly annoying, and it makes me respond by building random buildings all over the map so that I waste their time. Or when they do a couple of failed all in attacks that you hold off easily, and then they start trash talking you calling you a noob, etc etc, then messaging you after the game from several different accounts, but they have you blocked so you can't respond to them. I don't see the point of acting like a little child when you lose because you played like an idiot.