Both Eva and Miss Meg requested I recommend movies similar to The Bourne Identity (2002), which is one of my favorite movies (and franchises), so here we go!
If you like The Bourne Identity, with its exciting chases, helpful and brave love interest, and confused hero who's not sure who's chasing him, or why, then you might like any of these:
+ Dark Passage (1947) -- A convict (Humphrey Bogart) imprisoned for killing his wife escapes from prison to prove his innocence. Everyone knows what he looks like, so he gets plastic surgery to change his face so he can seek vengeance without being recognized all the time. He recuperates in the home of an artist (Lauren Bacall) who becomes convinced of his innocence and tries to help him. (This one has violence. It's film noir, so some dark themes and stuff that might frighten kids. Also, Bogie looks kinda creepy in his facial bandages.)
+ North by Northwest (1959) -- Classic Hitchcock :-9 Roger Thornhill (Cary Grant) is just an advertising executive. But a bunch of spies are convinced he's also a spy, and they try really hard to kill him. Over and over. And they frame him for murder, so the police are after him too. Then he meets Eve Kendall (Eva Marie Saint) on a train, they fall in love, and she tries to help him survive all this chaos. (Lots of double entendres in this one, most of which will entirely fly over the heads of kids. There's some violence, and intense/scary moments of danger and peril and suspense. I think also some more traditional cussing.)
+ Charade (1963) -- This time it's a woman who is being pursued and doesn't know why. Regina Lampert (Audrey Hepburn) learns, at her husband's funeral, that there are a whole bunch of people who want something that her husband had, but never told her about. They chase her all over the place, trying to scare her into giving them what they want. A CIA agent (Cary Grant) pops up to help her sort out the mess, and sparkage ensues. This one has topnotch villains, especially James Coburn and George Kennedy. (Mostly family-friendly. There's a little bit of suggestiveness here and there, double entendres and this silly game where people have to try to pass oranges to each other without using their hands, and a little kissing. Plus, Cary Grant in the shower. Possibly a couple mild curse words, and lots of '60s-style violence where it's not gory but still, people die and get hurt.)
And today I have a BONUS for you! Did you know there's another adaptation of The Bourne Identity? Yup, it was made into a TV movie in 1988, starring Richard Chamberlain and Jaclyn Smith as Jason Bourne and Marie St. Jacques. It sticks very closely to the plot and characterization in the original book by Robert Ludlum (which I reviewed here), and is overall very enjoyable. If you're like me and enjoy seeing different adaptations of stories, I recommend trying it. (There's some violence, no bad language I can recall but I might be wrong, and one love scene where Marie's in lingerie and Jason is shirtless and there's some rolling around on a bed or something-- I completely recommend that everyone skip that scene at all times, because although there's no nudity, it's embarassingly '80s-ish.)
What do you think? Are there other movies that remind you of The Bourne Identity? I've got a bunch of ideas for these posts, but as always, if you've got a request for something you'd like me to make recommendations based on, I love suggestions!