Well, being the heavy-emtional person that I am, of course I cried at certain moments.
There are three major places:
Prophecy Girl: when Buffy is crying to Giles that she's only sixteen years old and doesn't want to die.
Passion: When Giles finds Jenny's body, and when Willow gets the phone at Buff's house. In fact, I think I cried through the last half of that episode, as soon as Jenny died.
Becoming, part 2: When Buffy kills Angel, after his soul is restored and kissing him goodbye, and then when she walks away from the school after seeing her friends talking.
I'm just a silly, emotional person though. There are other times where I've cried during the series, but those were the major.