A wrecked vehicle sitting in your driveway is an eyesore. If it sits long enough, it also will leak fluids and create a physical and environmental hazard. It is best to dispose of wrecked vehicles that you have no intention of repairing or driving again. There is a huge market for wrecked vehicles because of demand for used parts, which are less expensive than new ones. There are several ways to dispose of wrecked vehicles.
Contact a vehicle salvage yard, also known as a junker. Many of these yards will pick up the vehicle and pay you a stipend. These types of yards will resell the vehicle for parts, so whether the vehicle is running or not is irrelevant to them.
Sell the vehicle for parts. List it online or in the newspaper as a non-running vehicle being sold for parts. Be sure to accurately list the parts and attach a competitive price. You can let customers pick individual parts off the car, or sell the whole car. You can also remove parts yourself and place an ad on an online auction site. If you allow parts to be picked off the car, will probably be left with the frame and most of the body at the very least, and you'll still need to get rid of that. A salvage yard might be interested in the leftovers.
Donate the vehicle to a charity. Some will accept non-running vehicles as a way of raising funds through parts sales. Be sure to notify the department of motor vehicles of the transfer. The advantage of donating the vehicle to charity is you can write off the vehicle's value on your taxes. Just be aware that claiming anything over $500 might cause IRS scrutiny. Contact the charity to get its final proceeds from the vehicle if you claim more than $500 as write-off.
