Here is the lowdown on the WDW thrill rides:
MK
Big Thunder Mtn - Tamest of the WDW coasters (except Barnstormer, but that doesn't really even count as a coaster). Small sudden drops and lots of sideways forces. No big drops or upside-down manuevers. Avoid this only if you can't handle ANY roller coaster.
Space Mountain - Lots of sudden small drops and sharp turns that cause significant lateral forces. Also, it's in the dark, so it's hard to brace for the manuevers. If you have back problems, you'll want to avoid this. It doesn't go upside-down or have major drops (no WDW coaster I have ridden has major drops - I haven't ridden EE yet, so it might - I don't know).
Splash Mountain - Three flume drops. The last one is major at about 50 feet, but it's really the only hair-raising part of the ride. The rest of the ride is so good that I would advise everyone to gather their courage and ride this.

You may get a little wet, but it's usually no big deal.
Epcot
Soarin' - I haven't ridden it yet, but the word is that guests of all ages love this. I understand that there are no extreme forces at all, just an incredible illusion of flying.
Test Track - The first part of the ride is bumpy in places and has some fairly strong lateral forces. If you have back trouble, you may want to avoid it. The final part of the ride - high speed "testing" - is smooth as silk.
Mission Space - If you can handle spinning motions, the launch sequence on this ride is INCREDIBLE! The only real problem is if you can't handle the spinning. Most people have no problem if they focus straight ahead, but you'll have to judge for yourself. This is a unique and very exciting ride, and if you can physically handle it, I would advise trying it. (NOTE: you won't
feel like you're spinning while you're riding it if you keep looking at your screen.)
D-MGM
There are
SERIOUS thrill rides here. These two are in a league of their own at WDW!
Rock 'n Roller Coaster - This is the best coaster at WDW. You will want to stay completely away from it. It launches you from 0 to 60 in 3 seconds and flips you upside-down 3 times (2 in the first 10 seconds!) I love it; you probably won't! (NOTE: it doesn't have any drops.)
Tower of Terror - This ride is actually very gentle in its motion, but it does "drop" straight down 30 or 40 feet, and more than once per ride. (It actually is pushed down, so it's faster than freefall!) If you think you can gather the courage to challenge the drops and can physically handle them, the rest of the ride is truly an amazing display of Disney magic!
Star Tours - This ride tosses you about. I have motion sickness issues with it (mild nausea, but nothing more) because of the up and down motions used, but you may like it fine.
AK
Expedition Everest - I haven't ridden it, but I understand that it is a high-thrill coaster. It doesn't go upside-down, but it's fast! Others may want to fill in, but I'm guessing it's on your "no" list.
Primeval Whirl - This ride is not nearly as benign as it looks. The lateral forces, especially during the spinning parts, are quite intense. The sudden drops are small but have impact.
Dinosaur - The ride is rough, but the primary thrills come from the sights rather than the ride itself. I think you'll like it if you don't have severe back problems.
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Just to fill in, my dw

is 42, but has serious back trouble from arthritis. (In fact, she needs to use an
ECV to go to the parks.) She is able to ride every ride at WDW except Space Mountain, which she finds to be too hard on her back. She has not ridden Soarin' or Expedition Everest yet, and she finds the final flume drop on Splash Mountain a bit too intense for her taste. She is not a roller coaster jockey like me, yet she loves RnRC!
Naturally, you should follow all warnings provided at each ride and use your own judgment regarding your health and your ability to ride based on them.
Tim, who hopes that you press your courage a little bit (if that's all that's holding you back). Adventure is part of what a trip to WDW is all about!

(Remember, for persons in good health, thrill rides and coasters only
feel dangerous!)