At IOA, you can't take your bags onto Dueling Dragons or the Hulk. Dueling Dragons lockers are free for 45 minutes and the Hulk for about 90 minutes. They only thing I've ever been able to take onto these rides is a small fanny pack. Popeye and Bluto's Bildge Raft Barges has a small area in the middle of the raft to store your gear and keep it dry. Jurassic Park River Adventure has lockers for about $1.10 an hour, but I've never had a problem bringing bags onto that ride. If you go on Pternadon Flyers, you need to keep your bag on the platform.
At USF at MIB, you're supposed to put your bags into lockers, but I've seen a few people slip by with bags. In that case, you need to put your bag on the hook or small pouch in the ride vehicle.
Every other ride I've put my bags on the floor or in the small pouch.