Wear cargo pants or pants with button/zipper pockets = problem solved. I've brought my phone/camera/wallet on all the Busch coasters (W-burg, Tampa, and Sea World) and never had a problem. My phone did slip out of my pocket on BGT's bumper cars and skyride though.
As for bags and such...
Alpengeist is incredibly lenient with bags on the platform. Some of my friends leave their backpacks on the platform all the time.
Apollo/Griffon are hit-miss. You generally can't leave backpacks/drawstrings on the platform, but smaller bags are fine.
Loch Ness/Verbolten are the most strict when it comes to bags. Leave them in a locker or with a non-rider.
Flat rides should have a place to set your stuff on the side (either cubbies or just leave them on the platform). Mach Tower is the only flat ride with restrictions and even they're pretty lenient.
I'm sure you don't wanna carry wet bags around, so keep them in a locker or with a non-rider for water rides. Setting them on the platform probably isn't a good idea unless you have a waterproof bag.
flip flops are to be taken off and placed on your seat for you to sit on securely
You can't take your shoes, flip flops, sandals, or other footwear off on Verbolten. I learned that the hard way.
- Or you could always just carry the essentials and not have to worry about taking your bags onto the rides