One of the awkward moments I remember the most was at one of my brother's parties when I was 16. I still remember it really clearly. I got bored of hanging around all of my brother's drunken idiot friends pretty fast so I went into my room to play Monkey Island 2.
Anyway, I'm at the part of the game where you have a drinking competition with the fat guy in the house, and then my door suddenly opens and this girl walks in and lies face down on my bed. I got up and closed the door, but then I tried to play it cool so I just got back on the computer and made a point not to look at her. About 5 minutes later though I decided to change tactics, so I turned to her and said "do you want a glass of water."
She didn't say anything. She seemed pretty drunk. She seemed like she was asleep, actually. I recognised her as one of my brother's friends and thought it would be funny if I played with her hair. Like she'd suddenly wake up and we'd laugh about it. I didn't even get to do that though because literally half a second later some guy opened the door, said "she's in here," and then picked her up and walked out.
I still think back to that party and think that if I wasn't so awkward and didn't sit on the computer for 5 minutes something could have happened there.