Everyone keeps talking about domain parking, but how much does it cost to park a domain name? What do the parking services charge for it? Could I make more if I shut down my sites and just parked the domains?
No you wouldn't make more unless your sites are just sitting there and you're not actively trying to make money from them. I think you're better off working on your sites yourself but parking is an option if you don't have the time to do so.
You shouldn't have to pay anything to park a domain and services like sedo are free to set up. It could cost you a lot in terms of earnings, since parked domains don't seem to do as well as ones with sites attached and the domain name's value drops.
Parking a domain is generally free, in fact they are services that will place ads on your parked website and give you a share of the ad revenue. In response to the second part of you thread, you won’t make more money by parking your websites as Google will lower your rank due to the lack of content a parked page had.
I think some of the domain management companies don't have any specific price. Some even give you ads for the domains. This means you can find that the cost of the domain may come up and down. That being said, SEDO and DomainPros offer such services. And it's worth taking a look into.