Hi Dianne! I hate big drops too, so I definitely understand where you're coming from! One of the reasons I love Disney World is that non-thrillseekers like us can ride most of the attractions there. Each park has only a few rides that you'd want to avoid if you don't like drops.
In the Magic Kingdom, you already know you don't like Splash Mountain and Space Mountain. Like you, I love Big Thunder Mountain Railroad because it doesn't have big drops, and I like Goofy's Barnstormer as well. I have to admit that I avoid Pirates of the Caribbean because it does have a downhill drop in the dark at the beginning; it may not bother most people, but if you're very sensitive to drops like I am, it would bother you.
In Epcot, I love Test Track and Soarin' -- no drops on either of those rides! The Maelstrom in Norway has a backwards drop, and Mission Space has simulated drops that may bother you.
In Hollywood Studios, you definitely want to avoid the Tower of Terror, which is a series of drops, and the Rock 'n' Roller Coaster. Some people have problems with the simulated dips in Star Tours, but they don't bother me.
Finally, at Animal Kingdom, you'll want to avoid Expedition Everest and the Primeval Whirl, both of which have some downhill plunges. I also don't like to ride Dinosaur because it seems to have a big drop at the end, although my husband insists it is only a simulated one and my kids say it doesn't have one at all. Kali River Rapids has some small drops as well.
With the exception of the attractions I listed here, you'll be able to enjoy all the other rides at Disney! Hope you have a magical vacation!