Can you bring bags on rides at Disney World?

Even though my kids are grown I still always seem to have a bag with me when I am at Disney World. I always have things that I "need" in the park, like ponchos and sunglasses and hand sanitizer. Sometimes my bag is a small crossbody and sometimes it is a packed to the gills backpack. I don't think I've ever gone into a park at Disney World without some sort of bag. But, what happens when you're touring? Can you bring your bags on rides at Disney World?