The vast majority of attractions at Disney World do not have drops. So let me just warn you about those that do have drops so that you can avoid them and enjoy everything else.
Those that have major drops are: Big Thunder Mountain, Space Mountain, Splash Mountain, and Goofy's Barnstormer in the Magic Kingdom; Expedition Everest and the Primeval Whirl in the Animal Kingdom; the Tower of Terror and the Rock 'n' Roller Coaster at Disney's Hollywood Studios.
Those few are the only rides that have ever give me "roller coaster stomach." But just to be safe, let me also point out that there are a few rides with more minor drops (all of them wet ones): Pirates of the Caribbean at the Magic Kingdom; Kali River Rapids at the Animal Kingdom; and the Maelstrom at Epcot.
Also, there are a few rides that go up and down, but you control the speed and number of drops: Dumbo, Astro Orbiter, and the Magic Carpets of Aladdin in the MK and the Triceratops Spin in the AK. These are all gentle rides meant for younger children.
Soarin' at Epcot and Peter Pan's Flight in the MK both include very slow, controlled changes in altitude. But they are not "roller coastery" in any way.