There are loads of moving scenes, but these are the ones I remember most, and why:
Movie: The ending of Donnie Darko, because after all the weirdness and attempts at understanding himself, Donnie met his end anyway. He seemed doomed from the start, but you wanted him to have a happy ending. It was the first film I watched with this kind of ending, so it moved me. I found the ending of Cruel Intentions quite moving as well, because it seemed so unfair that the character who had redeemed themselves and become a better person got killed.
Game: Aeris' death in FFVII. This was the first RPG I played, and I developed a real attachment to all the characters. To be honest I didn't really use Aeris in my party, but I'd grown fond of her in the story so when she died I was like 'OMG NOOOO', and she was the last of the Cetra too. The only other game I've developed a real attachment to the characters in was FFIX.
TV: The end of the last episode of Blackadder Goes Forth. For those who don't know it, Blackadder was a British comedy series where the main character was basically a bad guy, but you wanted him to succeed because all the people around him (especially his superiors) were idiots and he seemed to be the only sane person. The character Blackadder was always arrogant, sarcastic and full of malice, but you wanted him to win.
The series, 'Blackadder Goes Forth' was set in the First World War, and throughout it Blackadder attempts to cheat death through a number of schemes whereby he avoid being involved in attacks on the enemy. However, in the last episode it slowly becomes clear that there is no way out for him this time. In the end he bravely accepts his fate, and dies with honour with the rest of his men. The final scene is very moving if you've watched the rest of the series, that episode, or even if you remember the terrible toll that the First World War took on the UK in terms of its youth being ordered to charge into certain death.
Also, because the show is a comedy and Blackadder
always manages to get out of tough situations, this scene really makes an impact. Oh, and for fans of House, Hugh Laurie plays Blackadder's lieutenant:
http://www.youtube.com/watch?v=IglUmgYGxLM
None.