It is quite possible to wire a car stereo without a harness, it just makes the job much more difficult to perform successfully. The harness is available to make the job easier and hold the car stereo in place when the vehicle moves. Should you decide that you cannot afford a harness for the car stereo, then you should perform the installation process with a manual by your side in order to perform the job correctly the first time. If you do not have a harness you will need to connect the stereo wires directly to the corresponding wires, which are directly attached to the dashboard.
For more info, see Car Stereo Installation: A How To Guide