When I first started reading One Piece, I liked Zoro well enough. He wasn't one of my favorites, but he was a cool sword dude, and did his thing.
This is a cliched answer, but when Zoro declared to Luffy that he would never lose again was when I became a fan. The anime sold it well with Kazuya Nakai's excellent performance and Zoro's very human reaction. It convinced me that what he was fighting to achieve was very important, and that his standards of strength should be better than what he's displayed.
The fact he addressed it to Luffy shows he is a man of conviction, too, as he promised Luffy the strongest swordsman upon entering his crew.
My love of Zoro only grew as the arcs went by, seeing how far he is willing to go to achieve his dream, challenge the insurmountable. But his means of reaching the top differed from Luffy. It was steeped in discipline and far east ethics. Vivi's moniker of "Mr. Bushido" fits him to a T.