Well, according to me and the Internet Movie Database, though according to people here we seem to have missed a few. :-?
I have not by the least means seen these all, but will throw in a comment here and there on those I have.
Clothes Make the Woman (1928)
http://us.imdb.com/title/tt0018778/--One of the earliest tellings of the Anna Anderson story. If it's the one I'm thinking of, has Anastasia as a plucky flapper making a mad escape by automobile. Purdy hokey but interesting as being such an early film treatment of the story.
Rasputin and the Empress (1932)
http://us.imdb.com/title/tt0023374/Anastasia (1956)
http://us.imdb.com/title/tt0048947/"Hallmark Hall of Fame" Anastasia (1967)
http://us.imdb.com/title/tt0595265/Nicholas and Alexandra (1971)
http://us.imdb.com/title/tt0067483/--This was my introduction to the Romanov story. A well-acted drama, parts of which I still remember all these years later, and would like to see again.
Dulce Anastasia (1977)
http://us.imdb.com/title/tt0405891/Anastasia: The Mystery of Anna (1986)
http://us.imdb.com/title/tt0090638/--Presenting Anna Anderson's story as fact, but gets some details wrong. For instance, claiming AA's baby died, when a lot of the trouble was that he did NOT die and relatives feared he'd emerge to try to claim the throne. Also, showing the Romanov relative who kicked her out as being under family pressure rather than that AA acted like a flake while there. It was surprising to see Lord Louis Mountbatten, played by Rex Harrison, portrayed as such a baddie.
Rasputin (1996)
http://us.imdb.com/title/tt0117442/Anastasia (Disney, 1997)
http://us.imdb.com/title/tt0118617/--Yeah, I'll get around to seeing this when I see "Pocahontas"--whenever that is.
The Russian Revolution (Documentary, 1998)
http://us.imdb.com/title/tt0235723/--I remember seeing a documentary with a lot of old newsreel footage but don't recall if this was it. It's so neat being able to see films of the actual people!
--There was also a NOVA documentary on the Romanov bones and Anna Anderson.
Romanovi: Ventsenosnaya semya (2000)
http://us.imdb.com/title/tt0303274/The Revenge of the Romanovs (Documentary, 2001)
http://us.imdb.com/title/tt0395730/The Lost Prince (2003)
http://us.imdb.com/title/tt0349747/--I commented on this in the thread on "The Lost Prince," but would like to add there was one glaring inaccuracy in the Romanov death scene on which no one commented in that thread. Contemporary accounts state that Grand Duke Alexis was so severely ill he had to be carried by his father and was perhaps (hopefully!) only semi-coherent. This movie showed a boy looking perfectly healthy (and way happier than he probably should have under the circumstances--though of course they didn't know what was to happen until they entered the execution room and heard the order read--) WALKING. That just jumped out at me. Alexis was certainly in no condition to have possibly survived, or in shape to have helped himself after such an event if he was near death before, though why his body is not with the others remains a mystery.
Shadow Hearts II (2004)
http://us.imdb.com/title/tt0443635/--Anyone know what this is? Sounds weird.
Unsolved Mysteries: Strange Legends (2005)
--This is from a series of compilations from the TV series, grouped by themes. This one covers the Anastasia/Anna Anderson story. I found the execution scene to be MUCH more accurate than the one portrayed in "The Lost Prince." It may not have been filmed in Russia, but the people all spoke Russian, and Tzar Nicholas was portrayed as carrying Alexis. I would recommend it as an addition to any collector's library.