The Wonderpets were a favorite of my kids too. But I cursed them when the phone rang and I found myself singing, “The phone, the phone is ring-ing! The phone, I’ll be right there!”
I remember liking Charlotte’s Web a lot at that age, though there is the death of Charlotte…and the almost death of Wilbur…so…yeah.
I also loved the Winnie the Pooh movies/videos, whatever you want to call them.
Seconding Wonder Pets and anti seconding Max and Ruby. Ruby IS the aforementioned B word and Max is so incredibly…uh, special.
One of the first movies we watched with our daughter was the 1995 version of The Wind in the Willows. It’s quite mild but there are a couple of parts that have a bit of tension. (It’s hard to come up with a totally tension-free movie, but this one is pretty low on the scale.)
My almost three year old absolutely loved The Princess & The Frog (as did her Mom and I). It’s a really cute movie w/ lots of great music and characters. She didn’t really get what was going on, but it held her attention the entire time.
The next day she kept talking about the alligator that played a horn. 
I forgot all about ** The Backyardigans** excellent, but quite catchy.
be forewarned.
Heh, my wife is a Backyardigans addict. She likes it more than my four-year-old! 
Our boy is going through a phase where what he hates most is any conflict between the ‘good’ characters in the movies he watches - where one is unhappy at, upset with, or worse - fighting with another. He doesn’t mind "scary’ nearly as much, or identified ‘bad guys’ meanacing the ‘good guys’.
For example, he refused to watch Toy Story past a scene where Woody was fighting with the space-guy. That really bothered him.
Yes, the Wonderpets is my daughter’s current favorite and it is starting to get to me.
“And adult man…singing Wonderpets…this is sewious!”
As for the OP, we watched The Sound of Music recently with my daughter (almost 4) and she loved it! It is rather lengthy, so you would probably want to break it up a little bit and there was only the teensiest amount of peril at the very end.
We also have a couple Elmo’s World and Dora the Explorer DVDs that are essentially just 3 or 4 20 minute episodes on one disc. Those are nice because you can just limit the kid to a certain number of episodes as time permits but still have “closure”. She also likes that new Tinkerbelle movie, which has some peril but she doesn’t seem to mind it and she is a bit of a wimp.
This may be a bit above her age range, but I recently let my kids (ages 3, 6, and 8) watch Mary Poppins, and they really loved it, my 6-year-old in particular. The 3-year-old did wander off after a while. He has low tolerance for live-action movies.
And I’ll third, or fourth, or whatever we’re up to, the rec for My Neighbor Totoro.
Shaun the Sheep is excellent. It is a series of shorts, maybe 40 or so, around 5 minute long. Shaun is the sheep that Wallace and Gromit rescued in A Close Shave. The stories are simple, peril-free and told visually, with no dialog. Here is a sample from YouTube Off the Baa!.
I think most of them are available on DVD.
Mary Poppins is a great choice, MsWhatsit. I used to watch that one all the time as a small kid. And I think it’s something an adult can enjoy, too. Julie Andrews is a real treat. And Dick Van Dyke is awesome–OK, if you can get past the faux Cockney. I think he was my first crush, actually. I think it’s my all time favorite Disney movie.
I may even have some to send you as our daughter is too big - but maybe not the polka one. That one we still like…
I don’t know if she likes cars at all, but um, Cars is pretty tension-free. My 3.5 year old son looooves that movie.
WALLE* is fun - there are some tense moments though.
Then there’s Ratatouille, but although it’s not scary, it is more for older kids.
For some reason, I find Elmo in Grouchland endlessly watchable - but, again, some scary moments, and then there’s the whole “taking other people’s stuff thing” (Mandy Patinkin plays a selfish villain who takes Elmo’s blanky, and. . . oh, never mind).
Wow, this thread brought back memories - I was that kid too at one point! And if I had it bad, my brother was worse - he wouldn’t let me watch The Rescuers, one of my favorite movies, because the alligators scared him.
Everyone could agree on:
The Rescuers Down Under - which might be a bit much for your daughter, so I’d try watching it first and then seeing what you think. The scene where the albatross is injured, and then when the poacher temporarily captures the eagle might be too much peril. However, I’m sure she’d love (as we did) the scenes where Cody rides the eagle.
Fantasia - except for the very last segment, Night on Bald Mountain*, this is mainly just eye candy and a good way to introduce kids to well known classical music. The dinosaur segment (The Rite of Spring) might also scare her a little bit (it vaguely suggests extinction, and, well, it’s The Rite of Spring) but that one can go either way. Toccata and Fugue remains one of my favorite pieces of animation, it’s amazing to watch.
Disney Sing-A-Long Songs - it’s the songs from all the movies, with the words underneath so you can sing along so to speak. Nothing scary, for sure. If you can put up with that for long periods of time, my brothers and I loved them; we must have had nine or ten of the videos. (Actually, do these still exist? We had them in the early 90s.)
Really Rosie - Maurice Sendak and Carole King’s collaboration. The kids have an argument at one point but for the most part the tone stays very sweet and fun, and the songs are quality. If you like this, you might like the other Maurice Sendak video we had (Maurice Sendak library), where the author narrates animated versions of Where the Wild Things Are and (my favorite) In the Night Kitchen. There’s a Robert McCloskey one we liked with Make Way for Ducklings and Lentil too.
I would second Wednesday Evening’s rec of The Aristocats; the only scenes of peril are in the beginning where Edgar strands the cats under a bridge, and then later when Marie, the little white kitten, almost gets run over by a train and falls off the train tracks. Everyone is okay in the end, though.
Homeward Bound II: Lost in San Francisco and potentially also the first installment in the series, The Incredible Journey are a couple of heartwarming films about three pets who get left behind by their owners and have to make their way home. (Twice! I know!) The latter has a bit more peril, such as when Sassy the cat falls into a stream and then in the end when everyone fears that Shadow the Golden Retriever has died, but they’re both fairly light.
I liked Fievel Goes West but refused to watch An American Tale because it was too sad. Similarly, I would only watch All Dogs Go to Heaven 2, but that one might be a bit much for the kid (hellish imagery and very bad bad guys).
Let’s see, what else… Have you all seen Enchanted? The scene with the dragon in the end is iffy, but otherwise it’s a very sweet film. Lady and the Tramp might be good (the Siamese cats are mean but not very scary). We liked Bedknobs and Broomsticks but you might want to wait on that one.
*well, actually I couldn’t tell you how bad this is - due to our mother having censored it from us, at 19 years old, I still have not seen it.
If you’re really trying to curry a taste for film, with this child, wouldn’t it be better for her to come to it on her own, rather than you foisting it on her?
When she’s ready it will emerge. But she’s clearly not yet. I think what you’re doing might actually be counter productive to your end goal. Ease up.
Just my opinion.
Well thanks, I guess, but as I said in the OP, we’re not trying to ‘foist’ things on her, just trying to (a) think of things which might entertain her without frightening her and (b) help develop/reinforce her understanding that she is safe with us and that things on the tv can’t hurt her, which I think is is part of my job as a parent. This isn’t some bizarre experiment in desensitisation or an introduction to film theory for pre-schoolers, honestly!
Thanks again everyone for all the suggestions and for the warnings about specific content. I’m reassured that other people have encountered this. Mary Poppins was also on my rental queue although I suspect it will be too long for her at the moment. There’s lots of others I haven’t even thought of, though, which is exactly what I was hoping for. (She’s a huge fan of the Backyardigans and the blessed Wonder Pets, and Dora and Diego and… actually, it’s starting to sound like all she ever does is watch tv).
Balto
No suggestions but the OP reminds me of the time I took my four year old niece to see Chicken Run. For those of you who haven’t seen it, it’s set on a chicken farm. The chickens are the heroes and the owners are the villains. Early in the movie, there’s a scene where it’s Saturday night and the owners are inspecting all the chickens to decide which one hasn’t been laying enough eggs. One of the chickens is chosen and the movie cuts to the next scene which is the dinner table a couple of hours later with a pile of chicken bones in the middle of it.
So I’m thinking, “boy, I hope my niece doesn’t connect the dots here.” But she turns to me and very solemnly informs me “they ate the chicken.”
I have a 2 year old and a 5 year old, both boys. My older son gets that sort of anxiety when things look like they’re going bad for the main character. At that age he used to shut the tv off when he got scared. Here are the movies that work for him now:
Alvin and the Chipmunks (original and Squeakquel)
Cars
Up
Aristocats
Sound of Music
Chitty Chitty Band Bang (although he gets a little afraid of the child catcher)
Wall-E (watched it every day for at least six months)
Toy Story
Over the Hedge
Cloudy with a Chance of Meatballs
Bedknobs and Broomsticks
Alice in Wonderland (took a few sittings)
Flushed Away
Annie (but the very end still makes him squirm)
I normally just sit and hold him and tell him that it’s okay and everything is going to work out.
Pixar’s Short Film Collection should be a hit with her. Simple, delightful stories. And as adult, it’s really fun to watch how Pixar got better and better at animation.
KiKi’s Delivery Service is another good movie for a kid.