At it's core, the Bourne series is about two things: awesome ass-kicking and the main character's quest to figure out who he is thanks to some serious amnesia.

There's something truly compelling about a guy who's body is a competent killing machine while his head is still trying to figure out what's going on. Over and over again Bourne's face instinctively goes slack while his hands are crushing dudes' larynxes left and right, and it's a joy every time. 

The fact that he's still trying to figure it out after three films is kind of shocking given Hollywood's need to wrap everything up at the end of a film. Bourne gets little flashbacks, but never the whole picture. That's probably for the best, though, because it looks like he may have been a jerk.