Soarin' tricks your brain into thinking you are flying/gliding. It isn't frightening but some people get motion sickness. I take a bonine before I spend a day in the parks anyway since I know I can get green with motion but love rides.
Pirates- a short drop in a boat and then just floating through the rest of the ride. The drop is manageable for toddlers so even if you don't like the drop, it isn't bad enough to ruin the ride (I think).
Peter Pan- cool and not scary
Winnie the Pooh. Sweet and not scary. Hated by some because of what it replaced.

Its a small world. Unless you have a fear of dolls or HATE the song (that would be me).
Buzz Light year. In the dark, flashes and lights and the car turns from side to side as you shoot aliens. But there are no up and down type swoops or drops and it is really slow. Some feel motion sickness here too.
Haunted Mansion- dark and comic ghosts. No drops, nothing fast just a car on a track that rolls along inside the attraction. The ghost thing is a little scary for some young children (mine were always fine) and some adults just don't like the idea. But it isn't "creepy" scary. It is lighthearted, in my opinion.
Jungle Cruise- nothing scary at all except the standby line.
Magic Carpet and Dumbo are slow spinning rides. Not even bad enough to give me motion sickness. Not terribly exciting rides once you pass 8 years old, but some adults still enjoy them.
Mad Tea Party- Just NO unless you have a cast iron stomach. Even Bonine is useless on this thing.
Tomorrow land speedway. Nothing scary at all.
Under the Sea- should be fine
Disney World Railroad- nothing scary
Obvious bad ideas: Splash Mountain, Big Thunder, 7 Dwarves and probably Goofy's barnstormer