For a good number of rides at Universal, you are not allowed to bring ANYTHING with you that can not fit into your pockets. This is for your safety, and the safety of all the other riders.
Universal provides FREE lockers located all at the rides that you CAN NOT bring anything with you. This include:
Hollywood Rip Ride Rockit
Revenge of the Mummy
Men in Black
Hulk
Harry Potter FJ
and maybe some others that I can't remember.
Please, do not try and "hide" a fanny pack under your shirt or something to avoid putting them in the free lockers. I have witnessed a ton of people trying to do this that get turned away once they get to the front of the line. On some rides, like Rip Ride Rockit, I totally empty all my pockets, including my wallet and cell phone, because of the lift hill. THe first time I rode it, I almost lost my cell phone that was in my pocket because of that lift hill. The lockers are totally safe, and again FREE. However, they are not extremely huge, so I would stick with the fanny pack to put into the locker, and avoid bringing a back pack into the park.
Also, for some rides (like the water rides) they offer lockers for a fee. You are not required to remove a fanny pack on these rides, but if you want to keep them dry, they offer the lockers.
All rides, just like Disney, offer a place to park a stroller and they offer child swap as well if you don't want to leave the stroller, or if the child in the stroller is not tall enough to ride. Keep in mind the height for HP is 48 inches, so you might have to use rider swap (and thus not need to park your stroller) if the child in the stroller is under 48 inches tall.