Though majority of the parks do ask for an entrance fee, this is a one-time fee that is typically good for 7 days. Fees are generally inexpensive - around $7-$20 - and differ depending on how you enter the park (i.e., by car, foot, motorcycle, etc.). But here's the great thing - that's the most you will pay for the day. Once you are in the park, there's plenty of stuff to do ranging from hikes to swimming, and more!
If you like to visit several parks in one year, you should consider purchasing an America the Beautiful pass. This annual pass allows visitors to enter parks and waive all entrance fees. There are also discounted (or free!) passes for veterans and the disabled, so be sure to explore them all and see which one suits your needs.