If its just a regular sized backpack you plan to carry throughout the day you wont have issues. Most rides have a bag pockets on the back of each seat (Meaning the back of the seat infront of you is your pocket). If like the last poster mentioned is a roller coaster, you can put your foot through the straps and put the bag behind your legs so nothing falls out.
Also again as the last poster mentioned, there are lockers inside the entrance of each park that you can store your items in if you have too much to carry.
But there are so many rides like the Haunted Mansion, or Toy's Story, where your just in a moving car and your bag can be left by your feet or can sit beside you on the bench and it wont go anywhere.