I've never actually broken down in tears, but there is one scene in particular that always gets me right (punches chest) here...
Macross - Do You Remember Love. At the end, in the final battle, when Minmay is singing Ai Oboete Imasu Ka, and Britai and scores of Zentradi defect mid battle to support the Macross, and defend culture. There's just something about the beauty of the artwork coupled with the beauty of the song, and then they ram it home with the whole joining forces against a common foe thing. *sniff*