Robin's past wasn't too emotion-raising. Tragic, yes, but not really that tearjerking. Maybe that's because I haven't watched in awhile, though.
However, each of female crew member's (and Vivi's) Luffy-caused breakdowns were very emotional. Robin's in particular really made me love her more as a character. Vivi's getting ruined by 4Kids made me shun it utterly forever, and Nami's was rather touching.
Also, Nami's and Franky's pasts made me absolutely hate their respective villains (Arlong and Spandam). Chopper's sorta did, but Wapol using up Oda's ink made me hate him. I also was angered by the bomb scene in Arabasta. Vivi and the Straw Hats manage to pull a last-minute save, then Crocodile pulls one last aggrivating "gotcha," then Pell "sacrifices" himself, and then without missing a beat, everyone gets back up and starts killing each other while Vivi screams at them to stop.
Then again, episodes 120-127 (or whatever their corresponding manga chapters are) were pretty epic. Enies Lobby was awesome, but Arabasta showcases more of the epic storytelling that makes One Piece the bestest.