If you are handy with tools and have a bit of time on your hands, you could remove the car yourself. This option is best if the car does not run and you cannot find a buyer or junkyard that will take it for one reason or another.
To remove the car, you will need to disconnect the battery, drain all fluids, remove the tires, and then disassemble the rest of the vehicle. You can then put it in a dumpster or haul it away piece by piece.
Be sure to check with your local laws before removing the car yourself, as there may be restrictions on how to dispose of it.
However, if you are not able to dispose of your vehicle legally, there are salvage yards, such as 114 Auto Salvage, that might take away a shell of a car for free.