Rules are different at all casinos and change on a day to day basis.
Some charge, others don't, some charge only for valet. Some charge depending on the day of the week or perhaps as a result of an event day.
Many only require you to have a player card.

I personally don't let that bother me. I see myself going in to sometimes spend hundreds of dollars if not more. I won't let a few more dollars bother me.
I visited The Racino in Saratoga Springs as well as Empire Stakes in Yonkers N.Y. There you not only pay a hefty fee to valet park, you don't even get comped for drinks, in Saratoga you don't even get comped for the coffee.