Some of these suggestions are great, at least for my sensitive kiddo, but if you really want to know more about movies before you show them to your kid, check out http://www.commonsensemedia.org/ and read the reviews. I don't necessarily agree with them on the age range for each movie, but they give you a great idea of all the things your kid may or may not find problematic in the movie. And I suggest watching it yourself, first, because only you know what's likely to be scary for your kid.
My son LOVES Mary Poppins, but he did spend a lot of time processing the bank scene. We all love Little Bear. No conflict, fun plots, no annoying voices (unlike Calliou...). He also loves Mr Rogers. He watched Toy Story 1 a couple of times and is now obsessed with Buzz and spends a lot of time trying to process that Buzz is a Space Ranger who "comes in peace", yet he uses his laser. So anything with "bad guys" or people hurting each other or other creatures...the movie has to be really worth it to "endure" his constant questions and processing. :) (His daycare showed them part of Wizard of Oz this summer and that was NOT worth it...oy....)
Really, if your daughter is sensitive, I'd stick with Little Bear (there are quite a few stories on each DVD) and books-on-video from Scholastic (like Snowy Day). With those, and Mary Poppins, and some on-line Mr Rogers, I don't think you'll be lacking in something for her to watch when you want her to be doing that. :)
There are many great suggestions here. My daughter especially loves Peep and the Big Wide World, and Totoro. A few things she likes that no one has mentioned are Kidsongs and Big Comfy Couch (you can find both on youtube). Also the Harold and the Purple Crayon cartoon series, Wubbzy, and the Mr Men. She loves documentaries, the Planet Earth and Cosmos series and anything with ocean life, animals, etc. A few movies she's enjoyed, that really surprised me, are Little Miss Sunshine and Napoleon Dynamite, neither are really appropriate for a preschooler, but they both have great dance numbers at the end.
This has been most enjoyable to read and learn of so many more options. I will add that Wonder Pets on Netflix is a mainstay for us. It is quite creative, teaches kindness, patience and teamwork, and incorporates singing dialogue, similar to a broadway musical. We all love it!
-Ponyo, My Neighbour Totoro and Kiki's Delivery Service were all hits
-Singin' in the rain
-Sound of Music-until the kids go to bed
-Franklin and the Green Knight (blech, but the kids love it)
-Milo and Otis is on frequently too.
And it's funny, but Mary Poppins freaked out our LO (the floating on the ceiling, the bank scenes) for ages and ages. Only recently will she watch the whole thing!
Ds is also very sensitive with movies. Some that have worked for us are:
The Scholastic Video series (Love these)
Sound of Music (the first half)
Musicals of many types
-I love Danny Kaye and should introduce him to these
-I would imagine ds would like Singin in the Rain too
Cars (although we have to fastforward the combine/tractor tippin and the part the "mean" cars lull Mack to sleep)
Mary Poppins (fast forwarding the bank part)
Babe (recently watched this and it went over very well)
Charlottes Web (the old version cartoon)
I'm also surprised at the Nemo suggestion, this movie terrified ds.
We tried Chitty Chitty Bang Bang and that terrified him too (at 5 yrs). I don't think he watched more than 20 minutes total and kept hiding in the kitchen. I mean good gracious it has a "kid catcher"
Cars has been a big hit for a long time. My 3yo will sometimes ask for Nemo but leave the room for certain parts.
Our go-to safe videos (not necessarily full-length movies) have been Veggie Tales, Signing Time, and Cars, with the more recent addition of Kipper.
I will have to check out some of the other things mentioned!
HeatherB ~ mama to 3 wonderful boys: 03/02; 09/04; 09/07 - and Eliana, 11/13/10!
Founder of Houston Birth Alternatives: Be Informed, Encouraged, Supported birth support group and aspiring midwife.
Some Kippers are safe, some really freaked my Dd1 out when she was a bit younger. There is an episode about a ghost, one with little space aliens, one when they go to the moon....you have to pick and choose. I really do like them, though; they are kind to each other and speak politely.
We LOVE Pingu!
Mustard Pancakes (a sweet PBS show).
The first 2 seasons of Blue's Clues. Kind of inane, but harmless.
Little Bear. LOVE Little Bear.
Blue Planet documentaries (I appreciate these because the kills are not grisly and there are no copulation scenes that I have to explain. lol.)
The newer Charlotte's Web with Dakota Fanning - very true to the sweetness of the book, with only one fart joke. ;)
High-tech Hippie Mama to Dd1 (9/22/06), Dd2 (2/25/10) and Ds (05/27/2013). I eat Clean, cloth diaper, and spend way too much time online.
My kids are 5 and 3, and they were scared by Ponyo -- so much that they refused to watch it again! Ponyo's father is scary!
Finding Nemo was also too scary for them. :(
The only DVDs we've had success with are Peep and the Big Wide World and Richard Scarry's Busy People.