Even if tears formed just a little, put it out there! Would be a good idea to indicate the game, and if the moment is a spoiler, of course spoiler mark that part.
Endings of Persona 3 and 4: Knowing you and Aigis both learned something from each other- how to live. Then the human dies and the machine goes on living. Also leaving the town of Inaba after changing so many people's lives over the course of a year. Such a fulfilling game.
Ending of Shadow of the Colossus: No, not the tragic ending to our hero. For me, it's seriously when the eagle flies away from that garden and that beautiful music plays. I can't help but be overwhelmed every time I play the game and that moment happens.
Ending of Luigi's Mansion: Yeah, I'm not kidding. This isn't a joke. Maybe it won't affect me now but when I finished that game as a kid and Luigi finally rescued his brother, and all he could do was burst out laughing in tears when Mario got the painting stuck on his head...it...I don't know. It affected me. Please tell me I'm not the only one!
Also...Anything involving Vivi in FFIX, pretty much.
There's probably more examples but here's some just for starters.
EDIT: In Bioshock Infinite. The guitar part. It's just so beautiful.