It's not surprising that most movies made about the Romanovs have embellished or completely made up the story, which is very surprising to me. After all, this story has enough drama based on the facts! Two movies stand out, one slightly more
"Anastasia" is a 1997 animated movie from Fox. This movie illustrates two points: 1. Sticking to history - and reality - isn't such a bad idea, and 2. Fox really can't compete with Disney when it comes to animation. In this movie meant for children, Anya is an orphaned teenager who wants to find her family, so she leaves the orphanage and accidentally stumbles into the royal palace, where two con artists hoping to cash in on the dowager empress's reward money, see the similarity between her and the imperial children and train her to say all the right things. Oh yeah, and Rasputin comes back from the underworld to curse Anya because she escaped from death. Anya is of course the true grand duchess, and ends up falling in love with one of the con artists. Even when I was young, this movie made me cringe. (And yet, do I still have the soundtrack and occasionally blast it when I'm driving for fun? Perhaps.)
"Nicholas and Alexandra" is a 1971 film that, being based on the book of the same title by Robert K. Massie, is much more historically accurate. It also includes Russian society and the depravity of the everyday lives of normal Russian people - giving context to how the Revolution came about. I loved the portrayal of the relationship of Nicholas and Alexandra, which was one of the most enduring marriages among royalty, rivaling that of even Alexandra's grandparents, Queen Victoria and Prince Albert. The movie also focuses on Alexei's hemophilia, and Rasputin is heavily featured, creepy as ever. The acting is slightly melodramatic, though in the typical style of those days. If nothing else, I appreciate this film for the way it sticks to the facts, minus a few minor tweaks.
There is also a 1956 film called "Anastasia" with Ingrid Bergman and Yul Brynner. It is based on Anna Anderson's story, which I am fundamentally against promoting. I have it in my Netflix queue, but haven't decided if I want to see it. I mostly like historicals that stick to what happened.
If you're looking for nonfiction material, there unfortunately aren't very many out there. The one I have seen that I enjoy is only available in VHS form, though I very occasionally see it on the History Channel. "The Revenge of the Romanovs" earns points because it includes home movies of the Romanovs themselves (without sound, of course), as well as interviews with the men who found the family's grave outside Ekaterinburg. It also shows scientists analyzing the Romanov bones, as well as the state funeral the family was given in 1998.
I'd love recommendations of other movies or documentaries!