While nothing has made me outright cry, some things brought a tear to my eye. For example, and I'm probably going to get a lot of criticism for this, there have been some moments in Dragon Ball Z and Yu Yu Hakusho that brought a tear to my eye.
Now let me be perfectly clear. I've seen numerous movies, read numerous books, and heard numerous songs, and by some sort of irony, it's those sorts of anime that can impact me at times. It's usually, if not entirely, the moments where a character's loved one(s) is killed before his eyes, and there is such great sorrow and anger that they completely let go of inhibitions, conscious or otherwise, and release the power dormant within them. That concept seems to hit me more than most others for some reason, cliched as it is.