I just watched this movie recently after not seeing it in about a decade and I have to say, it's so weird watching a movie at an age where you can understand everything and your last memories of watching it, you couldn't.
Anyways, though, here's what I think about Anastasia.
I'll start with the story. Most people know that the story of Anastasia is based upon true and very tragic events, and that in reality, Anastasia was brutally murdered along with her family. I think that had already been discovered before this movie was made, making this kind of an odd subject to make a kids' movie out of. I do want to say, though, to parents who are concerned about the historical inaccuracy, don't be. I watched this movie between ages 2-5 and when I eventually found out Anastasia had died, I wasn't traumatized to find my favorite movie princess had been killed. It wasn't upsetting, I don't even remember it. As a kid, I never viewed the movie as a reality even though I knew it was based off a real mystery, it really was just a movie to me, and one of my absolute favorites.
The music in this movie is lovely, and a big reason for why I loved it so much. I was really touched emotionally by a lot of the songs and they stuck with me, it was great watching it at 18 years old and still being able to sing all the words even though I haven't heard the songs for years. I was really really scared of Rasputin as a kid, though, so his song, "In the Dark of the Night" brought not-so-nice memories and even put me off of a Queen song when I was young because it reminded me of it.
Rasputin is a lot scarier than most villains in kids' movies. He is described as a corpse, and is falling apart for most of the movie. As a very squeamish kid, this horrified me. His eyes and body parts fall off, and at one point, his hand reaches out and his veins stretch far like elastic (still made me cringe watching that part as an adult). Twice, his skin is blown completely off his bones. He threatens Anastasia and her friends' lives twice, once on a runaway train and another by giving Anastasia pleasant visions in her sleep when in reality she is close to jumping off of a ship during a storm (that particularly creeped me out as a kid). Anyways, as scary as Rasputin was, it didn't put me off the movie, I just knew when to close my eyes and I did so I could enjoy the movie as a young child and not be upset by it.
Nothing sexual comes to mind. Anastasia and Demitri share a kiss, Vlad subtly seduces the grandmother's servant to receive a favor in return (this went over my head completely as a kid, it's not worrisome.)
This isn't simply a feel-good princess movie, it's really an adventure movie. Anastasia is a strong female character who is determined and independent, definitely a good role model for young girls. She's depicted to be both beautiful and graceful while being very strong, humble, and brave.
Overall, I still love this movie and I'm glad I watched it again recently. The animation is beautiful and so is the music. Rasputin is scary and strange, but I was as squeamish as it gets and it didn't make me hate the movie. I think this is a great one for both boys and girls alike, as I said, it is an adventure movie for all audiences. I have so many happy memories of it that I'm grateful for all these years later, so I'd recommend it for kids around 3 and up.