It depends on the park and the activity. For example, Great Basin National Park has no entrance fee, but does have fees for a cave tour, campsites, and RV dumps.

In my experience, the vast majority of public land (forests and BLM land) is free to enter and recreate on if you aren’t using services like a campsite. National parks are more likely to charge entrance or parking fees but you are also more likely to get things like trash service and paved roads.

That being said, it’s still pretty cheap. You can get an annual pass for $80 that covers you and everyone in your car.