The answer to the question depends on several factors. One critical issue is if the vehicle was subjected to improper towing procedures that
caused the damage. If the damage is not directly related to the towing procedure it can be much more difficult to be compensated.
In general there are always options to file a claim with your insurance company or to take legal action against the towing company itself through small claims court. In cases of extreme damage to the vehicle or if the vehicle is rare or expensive you may have to take legal action beyond small claims, but for this an attorney is highly recommended.
The main obstacle for most individuals in this type of vehicular damage is to be able to prove the damage was caused by the towing company. If the damage is tow related this is typically much easier, especially if you have pictures or other documentation that the damage did not exist on your vehicle before towing. However, if the vehicle has damage or has been towed in the past it can become more problematic.
If you can prove that an incorrect towing procedure was used with your vehicle you have a much stronger case. An attorney that specializes in auto accidents can help you evaluate your case and collect the documentation and evidence needed to be successful. Often these cases can be settled out of court, with the attorney acting on your behalf in negotiations directly with the tow company.