You can take it on all the rides, including the thrill rides.
Keep it out and keep snapping away (without flash). There are some great picture opportunities on the rides! If you have a fast lens, bring it for the dark rides.
There are only a couple rides where they don't want you taking any kinds of pics--Rock n Rollercoaster, Soarin.... I think maybe Star Tours, too. They provide pouches where you can store the camera. For RnR, I usually just put the camera in my bag and wrap the bag's strap around my leg and wrist. I've actually taken a tripod with me on RnR. (Not to use on the ride, obviously, but just because I was carrying one around that night.) It was fine.
Disney's a great place for photography. They are very photographer friendly, and the wide range of conditions is excellent for practicing. There's motion, low light, bright sunlight... opportunities for wide angle, telephoto... huge park icons, small details... and of course tons of color. Have fun.