We went on green Mission Space last week for the first time. No spinning. The motions that I remember were being laid back on our backs in preparation for liftoff, rotated forward, rotated from side to side (like an airplane banking) and being rotated forward. I enjoyed it, but it was a little intense for my 8 year old daughter and my wife, who suffers from claustrophobia, didn't like it.
I want to try Orange next!
Edit: I forgot one problem that I had. When the ride is over, the shoulder bars are released automatically and swing up quickly. When the should bar popped up, it pulled my hat and glasses off.
Also, you have to stow your backpack or purse in a bin in front of you and its inaccessible during the ride. Make sure you don't have much in your pack, since the bin isn't huge.