Cars must be re-registered annually. If you have "been mailed a notice of delinquent parking violation relating to standing or parking" you will have problems with registration. The unpaid fines get tacked on to your registration fees. You can pay the DMV or pay the appropriate local agency. If you don't pay them, the Dept. of Motor Vehicles will refuse to register your car.
In addition, some municipalities will "boot" or tow a car that have more than X paid tickets. In Los Angeles, it's 5. (A boot is a device placed on the car wheel. The car can't be driven until the boot is removed. To get it removed, you have to pay the fines.)
In some cities, including my own, parking enforcement has cars that drive around with cameras aimed at license plates. The plate number is fed into a computer. If there are unpaid tickets, the boot crew is notified. If the car has been reported stolen, police are notified.
It was pretty embarrassing when the mayor of a nearby city had his car booted for unpaid tickets in Sacramento, the state capitol. It made the news because the manager of the mayor's opponent in the upcoming election happened to be driving past just as the mayor's car was being booted. Naturally, the media were notified.
Edited to add: the state can also deduct unpaid ticket from your state income tax refund.
Some states, according to a CNN article are now suspending drivers license for unpaid parking tickets.