Cars are for many Dentonites a primary mode of transportation. Cars are convenient and fast, and go where the buses don't. If you plan on staying in Denton though they aren't really necessary unless you have special requirements, and when you need to go somewhere in a car like Dallas or Fort Worth finding a friend who owns one isn't hard.
Near the Square
Parking around the square is free. There is also a large parking lot just east of the Wells Fargo Building.
Finding parking during the Arts and Jazz Festival can be problematic—to find a spot show up early. You can count on people not wanting to get up in the morning.
Parking at UNT can be a nightmare. And you either need to buy a permit or pay for metered parking.
There is free visitor's parking by the student union. There is also a permit you can purchase to use the other parking lots.
where else is there?
Towing is like legal robbery in Denton. Towing companies monitor their lots like predators watching their prey, so if you think you can park in a towing-lot for just 5 minutes as you run into someone's apartment, expect to get towed eventually. Towing companies in Denton include Two-Step Towing, On The Road Again Towing, and Bob's Towing. You can find the Texas Statutes on Towing here: http://codes.lp.findlaw.com/txstatutes/OC/14/A/2308
There are also a few companies that do towing as a service for people who are broken down or actually need to be towed for some reason, like Pro-Tow.