My son is 5. We don't watch a lot of tv. I let him watch up to 45 minutes of tv shows or one movie at one time. We often go weeks without watching tv at all. However, if he is sick I sometimes let him watch more. We have made discs of his favorites. He likes a lot of the shows that are on Disney Jr. and a few on cartoon network.
His current favorites are Special Agent Oso, Octonauts, Curious George, and Dinosaur Train. Dinosaur train is watched on my computer. He likes the games for Dinosaur Train. He will also watch Olivia, Clifford The Big Red Dog, Gazoon, Thomas the Tank Engine, The Bear in the Big Blue House, Poo and Friends, Little Einsteins, Barbar, Charlie Brown and Snoopy, Mickey Mouse Club House, Handy Manny, Elmo's World, Word World, Gaspard and Lisa, Jungle Junction,Timmy Time, Koala Brothers, and Wiggles. Plus a couple of Japanese cartoons, Hamutaro and Anpan man. I prefer to show them to him on disc, rather than watching all the commercials too. When he watches Wiggles, he usually dances while there is music playing.
He also loves watching documentaries on trains, cars, dinosaurs, animals, sea creatures, and travel. My husband and I always preview them for any violence or inappropriate language or mature topics. My son loves the series Mutant Planet (documentaries on weather patterns, geology, and animals of a particular country: He loves the one on New Zealand with the Kakapo.) He also liked Animal Planet's series on the Big Cats.
As for movies, we usually go with Disney/Pixar such as the Cars movies, Toy Story movies, Finding Nemo, or the Ice Age movies. But his favorite has to be Totoro. He was super excited to see Totoro in Toy Story 3.
I am fine with him watching the shows on Disney Jr. I know a few of the kids in his Sunday school class at church are watching things like Harry Potter and Star Wars, but I think that it is still a little early for those. I am sure that they would scare my son too much. He is afraid of Eve in Wall-E, and Kungfoo Panda is a big no-no. When the leopard first appeared, we had to turn it off. Even so, he had nightmares for weeks. I will probably introduce Narnia to him first, and then only through the books until I am sure he won't get nightmares. Last year at Christmas, I read him Mickey's Scrooge story. He was terrified of Marley, and we had to get rid of the entire collection of Disney Christmas stories. I love Dicken's Christmas Carol and thought the Mickey Mouse version was cute, but I won't be getting that back out anytime soon.
Go with the shows you think are appropriate and as long as she likes them let her see them. I know my son doesn't mind seeing the same episode again. He even uses the shows as a jump off for his pretend play. I love Oso. Oso and his three special steps can get my son to do just about anything once he starts to protest and helps us stay focused on what needs to get done. Watch the shows together and they can often give you ideas how to try something, or avoid a tantrum by engaging in a talk about something your child finds interesting. Hope that helps.