Most of mine have already been posted, so time for a quote-a-thon!
I will say first that I agree about the poster's scene from Gears of War 3. Such great use of music there. Good stuff. That series pulled a few good ones starting with the second one; I was rather impressed.
Casual Shinji said:
The ending cutscene from Shadow of the Colossus was pretty damn bittersweet.
One of the greatest endings in gaming, in my opinion. The use of inevitability there, where you have control of the character but are ultimately powerless, is freaking brilliant. Such an incredible game.
natster43 said:
The end of Professor Layton and the Unwound Future. It is the only game that made me tear up.
The actual cinema starts at 3:28
Professor Layton has always been awesome, but this was the first one to really bring on the tears for me. Holy crap, it was so good. The only other Professor Layton thing to make me come close to crying was the movie, which was good, but this scene still takes it all.
But in the end, only those who have played Clannad (or watched the anime based on it) can possibly know the true meaning of a sad video game. Clannad rips your heart out, rips it into pieces and stomps each of them into the ground, then slowly stitches it back together completely without painkillers. It's so incredible, so tragic, yet fulfilling and happy... it's astounding.
I won't post any videos because I don't want to contribute to spoiling anything, but I will mention one thing for those who have or will play it: Ushio in the flower field. Never has there been, nor will there be, a single scene so bittersweet and tragically touching in the history of everything.