I think Chopper's arc was definitely the most gut wrenching, emotionally draining character back story. It's just the fact he's so friendly and gets treated so badly; even Doctor Hiluluk dies. The anime totally captured Chopper's character and the magical, seasonal surroundings of his home.
Nami's Arlong Park story was absolutely captivating too - if fairly brutal (trying to scrape off a tattoo with a knife in a fit of rage) - for the first time it really emphasized the danger of their travels and the bond between the Straw Hats; the lengths to which Luffy is willing to go for his nakama.
Ramadahl's made a good shout with Logue Town too. It's easy to forget because it's such a short arc, but it rife with drama, mystery and just pure adventurous fun. It's very much the climax of the East Blue voyages and brings together many interesting characters for the first time (it was great to see Buggy struggling his way after Luffy!) - not to mention some very memorable flashbacks to the execution of Gol D. Rodger. Logue Town has this great moment at the end where all the characters, moving forwards through the sea, announce their dreams to each other. A similar thing happens when they enter the Grand Line for the first time. I love that kind of sentimental ambition.