There are many many moments that made my vision all blurry, I couldn't name them all, but I can list a few.
-The end of Jack's romance when she finally reveals her weaknesses to you.
-The end of Thane's romance when he finally reveals his weakness to you.
-The very end of the final cutscene after the suicide mission, with that grand orchestral swell and the reapers bearing down on the galaxy for the final confrontation in the next game...man, that is too much epic for me to handle, so much it leaks out my tear ducts.
-The end of the opening mission on earth, where the kid dies and Clint Mansell's score starts showing off. It's effective, dammit.
-The first time I played ME3 I didn't have grunt (never woke him up in my first game of ME2), so the mission on the Rachni planet was led by some unknown and totally forgettable krogan soldier; and damn if I didn't well up when he went charging into the Rachni line with heroic but dooming music sounding over his glorious sacrifice. Fantastic moment, that I honestly think was a bit cheapened the next time I saw it and Grunt survived somehow.
-That whole pre-ending section on the Citadel where you and Anderson confront The Illusive Man is amazing. After it all goes down and The Illusive Man is dying, Anderson is dying, Shepard is dying, the whole sequence until the platform ascends makes me feel things.
-And fuck off if you don't like it, but the ending made me feel too. It is presented well enough for me to overlook the flaws (which are honestly blown way out of proportion) and just appreciate the finale to my favorite game series of all time.