Leaving Earth, when that kid died (and before I knew the Catalyst was going to take his form) I actually shouted "NO!" in horror.
When Grunt died, or I thought he had, that hit me hard too.
Jeff and Liara at the end, trying to escape the Crucible's blast. Liara and Jeff's expressions just hit hard.
And finally at the end with Kaiden putting up Shepard's placard on the memorial wall . . .
I don't normally get torn up by movies, books and video games. But ME3 was effective. I think it was as much the music as the storytelling though.