We watched The Bourne Identity last night, DVRed it from the night before so we wouldn't have to watch commercials. Great movie! It makes you want to watch the other two Bourne movies.
Not to give away the plot for those who have not seen it, but what has happened to Jason is called Dissociative Amnesia. Amnesia either has a physical cause (brain damage or brain disease), the most common cause, or a psychological cause, as with Jason. It can be amnesia of the event and surrounding events or amnesia of one's entire past.
The brain tries to "protect itself" from a psychological event that is too difficult to cope with, by "forgetting" it. Again, not to give away what happens to Jason, but it obviously qualifies. The trauma can happen to you or you can witness it.
Occasionally, psychological amnesia is called Dissociative Fugue. Fugue is Latin for "flees." In addition to experiencing amnesia, people finds themsleves in a new life-situation and take a new identity, not knowing who they are or how they got where they are.
Does the memory ever come back? Sometimes it does, sometimes it does not. The brain has a memory technique called "priming." It is like priming a pump to get it to pull up water. (Kids, ask your parents what priming the pump is.) The brain can use familiar memories that surround the hard-to-surface-memory, to bring it to consciousness.
Does Jason Bourne's memory come back? Sorry... you'll have to rent the movie and find out for yourself.