Very appealing on a couple of levels *Spoilers* Please don't read this unless you've seen the movie.
I've seen this movie a half-dozen times now since I got it and I think I've figured out why I keep finding it appealing and entertaining.
At one level it's a pretty good popcorn thriller with gun-play, fights, car chases, the whole nine yards. There's a pulsing, tense, driving electronic score with some good strings thrown in that supports the sometimes over-the-top action scenes. We've seen it all before but it's done well and it works.
But at another level we have a story of a guy who wakes up after being pulled out of the ocean (literally born, get it?). This guy doesn't doesn't know who he is, who his parents or family are, where he came from and he can't remember any event in his life he experienced before he woke up. Despite all this, he can read and write, speak many languages and kick butt on anybody who dares to mess with him. He has survival skills to die for. To top it off, he has an led display sown into his hip that a displays a swiss bank account number full of cash and passports that allow him to travel anywhere and assume any identity he would ever need!
So in the process of trying to overcome his amnesia, he meets a young woman who seems to be only marginally better off than he is. She is rootless and currently homeless, living out of her tiny car. She has lived like a gypsy flitting from one place to another in a seeming quest to find out what she wants to do with her life. It turns out that each has something to offer to the other. He has cash, a Paris apartment and an amazing resourcefulness that is a mystery to them both. She has a car to help him elude the shadowy people who are chasing him. She also has an intact memory of her life which will help him in a critical way towards the end of the movie.
We identify with the Bourne character because all of us are born into the uncaring world helpless yet with some innate skills. We acquire language and mobility in a way that is amazing and mysterious to anyone who has ever had kids, yet we also need help. Bourne finds himself "re-born" into the world, gifted in many ways yet unable to really survive without help. The woman he meets becomes a sort of mother to him and enables him to find his feet in the hostile world where he finds himself.
I think we've seen this sort of story told before in many ways but I credit Ludlum for placing it in the spy thriller context.
Oh and by the way, the boy does get the girl at the end of the movie. What more could you ask for?