Most rides have little compartments or nets to keep items in. But they usually are kind of small. If your backpack is on the big side, I'd recommend trying to find a smaller one, unless you don't mind holding onto it on the rides.
The only ones that don't have compartments are Tower of Terror, Big Thunder Mountain, Rock n Roller Coaster, Splash Moutain, and Expedition Everest. On these rides, if everyone in your party are riding, you can simply slip the straps over your legs. That will keep it from moving around too much and will keep it with you. Either that, or you could just keep one hand on it during the ride.
The less intense rides, like Peter Pan's Flight, you can just lay it at your feet. It doesn't get jostled around.
Have lots of fun!