Aida - The final time I saw it, about a month before it closed, was when I cried the hardest. It was a mix of my favorite show at the time closing and getting to see Adam Pascal in person.
RENT - Everytime I see the show or the movie, I bawl at the I'll Cover You reprise, Your Eyes, and Finale B.
The Phantom of the Opera - Everytime you feel bad for the Phantom is usually when the tears start flowing. You just want to get up on stage and give the poor guy a hug.
Sweeney Todd - I didn't cry because I usually don't the first time I see a show (RENT was an exception), but I was so close. It was usually Tobias that had me choking up (Not While I'm Around, when he starts crying, and the ending). Sweeney had me in such shock that I couldn't cry (if that makes any sense).
There are also shows that have had me in tears due to laughter (Spamalot and Avenue Q). =P
"Nothing's gonna harm you, not while I'm around" - Tobias, Sweeney Todd
Yeah, yeah, I know all good things come to an end, but must Sweeney Todd end so soon?!