I'd love to say that Alys' death moved me. But my game crapped out on me before that could happen.
Major Spoilers in my post. Be warned!
Uhm... what else?
Lunar: Silver Star Story complete:
This was one of the sweetest victories that I've ever seen. Of course, it's sweeter in context, but hopefully you'll get my gist. Lunar pulled off one the the best "Happily Ever After" endings without being the least bit cheesy. (Okay, maybe a little.)
This moved me too. This is from Chrono Trigger for the psX. Seeing Chrono and Marle getting married is one of the sweetest things that I've ever seen in a video game, and the animation and music that was added in the psX version made it just perfect! I also love how this version seemed things up with Chrono Cross at the end. Nice!
This scene contains uber spoilers for Chrono Cross. Watch it from 8:10 onwards, it's really emotional then. Square almost made me cry. T_T
Spoiler time for Skies of Arcadia:
"His name was...Jack."
An even better scene. Drachma's story just moved me. The vids will explain it much better than me, take a look!
I know that I can think of more, but not right now.