Though I haven't beaten Shadow Hearts: Covenant yet, two scenes that have always gotten me were (SPOILER)when you find out why Albert Simon had really attempted to control Amon within himself in the first game, and the small conversation between Simon and Yuri inside Yuri's subconscious when he goes to reawaken Amon.
I've also always thought the beginning to the first Shadow Hearts was one of the best openings I had ever seen.
The speech that Yuna gives at the very end of FF X, (SPOILER)and the sequence of Tidus and Jecht sharing a high five at the very end always gets me. The music that plays while you're on the road going towards Yunalesca's stronghold always gets me too.
The ending sequence to Xenosaga Episode III.