I have taken my film SLR with me on numerous trips, and I bought a Canon Digital Rebel just before my most recent trip.
I don't carry a bag with me. I carry the camera on a wide, comfy cloth strap with a good walkaround lens (for my film camera I have a 28-200, for the digital I am currently using the 18-55 kit lens it came with but will upgrade soon).
In my pockets or hanging from my belt, I carry a spare memory card, my Speedlight flash unit, my IR remote shutter release, mini tripod, and a camera poncho made from a gallon-size Ziploc bag.
Not cvarrying a bag helps me to get through the park gates faster, but it also helps me to keep from carrying too much junk with me in the parks. If it can't fit in my pockets or on my belt, it doesn't go with me.
On most rides I can leave the camera on its strap around my neck and shoulder, but on a few I take it off and hang it between my feet.