I've been heartbroken, maybe a glint in the eyes from certain shows, but mostly just pain in the chest and a lump in the throat. but never straight up cryed my eyes out, but I think the ones where I actually grab my chest from the hurt is the best.. As for what shows have physically done that, well most of Joss Whedons stuff has had at least one moment during their runs (Bufy had Season 2 "Close your eyes," 5 - Joyce and Buffy, and 6 - Tara). Terminator The Sarah Conner Chronicles watching what happens to those characters (like John's forceable loss of innocence) made me realize that all the terminator movies where useless compared to this show.
Gurren Lagann - Lagann-hen (the 2nd movie) basically the same seen but they added 1 extra minute of character development both before and after that really just hit it home, of course Diebuster, Magical shopping arcade, damn you gainax. Now and There Here and There for obvious reasons, Kiddy grade I think because of the contrast of how it started off to what had and continued to happen to the characters.
Most recent one that kinda snuck up on me and hit me really, really hard was Darker than Black, knowing that something happens (Season 2) does not prepare you to watch as the inevevitable slowly happens in front of you eyes (DTB: Gaiden), yeah those 4 episodes were 4 episodes of pain.
And yet I actually watch as many of these sad, emotionally destructive shows on purpose, probably because life never offers anything as dramatic, without being as equally devasting.