First off, aint nothin' really free. Parking is actually extremely costly. Real estate sure as hell aint free, so how could parking on real estate be free? Additionally, if multi level parking is available, add the cost to build and maintain that structure. So who pays? The government? Perhaps, but guess who pays the government.
There's more than one problem with free parking. The major problem is it costs everyone, not just the user. So, if you don't own a car, your still paying for the "free" parking through taxes, higher prices and other hidden costs. The cost should go to the user through fee-based parking.
Another problem with free parking is that it encourages people to drive downtown. When parking is free you'll see people driving instead of taking the bus, walking or biking. Worse yet, is people will actually circle the downtown looking for the ultimate spot which causes undo congestion and needless pollution.