One of the things I liked about Star Wars: The Old Republic right from its launch is that it gave players plenty of antagonists to fight. Not just plenty of villains, mind you, but plenty of antagonists. Even if they had no role in the story beyond being a thorn in your side through a particular questing area, you had no shortage of characters who you wanted to drop just from a narrative standpoint.
But part of the fun of MMOs is that your antagonists need not sit there due to the game’s narrative. My greatest antagonist in Final Fantasy XIV for a long while was Titan, because at launch I was in a guild that just could not seem to get him down. I felt like our fight was intensely personal. My wife and I went out for ice cream when I finally beat him as a celebration.
And of course PVP can produce all sorts of entertaining rivalries – I know EVE Online players waging price wars with other players for years without firing a single shot. So between all of your many options, antagonists borne of game mechanics, PVP, or just the established narrative, who has been your favorite? A rival player? A major lore enemy? A difficult boss? Or even something more abstract, like a jumping puzzle?