Playing as a more serious cousin to the James Bond franchise, the Jason Bourne movies feel far more grounded in reality, albeit one in which Bond-like plots to undermine the CIA and destroy the world order drive the central narrative along. Matt Damon did a superb job of crafting the character over the course of three movies, and certainly gives any of the Bond actors a run for their money when it comes to portraying cool on-screen spies. Bourne's survival by the end of The Bourne Ultimatum without having to fire a single shot is something even the legendary fictional British agent has never managed to pull off. With Matt Damon no longer involved with the franchise it's unlikely we'll get to see him go one better in a future installment, although Jeremy Renner, who starred in the recent The Bourne Legacy, has said in interviews how much he'd love to do a Bourne movie with Damon, so there's perhaps hope he'll return to the role in the future.
