There are some upsides to single car accidents. It's unlikely that anyone's going to sue you over one and you don't have to worry about whether people are injured or if you're going to have to pay for damages to their car. On the other hand, it also means that nobody else's insurance is likely to pay out for your damages, either. 

The real silver lining is that it is, oftentimes, entirely up to you how you want to proceed following the accident.

Determine Fault

Not every single-car accident is the driver's fault. Yes, most single-car accidents are a simple matter of someone running into a light pole or a fence, but that's not always the case. It's not totally uncommon for a single-car accident to be the result of someone else's negligence. Sometimes a single-car accident is a result of another driver swerving or changing lanes without signaling, creating an "unavoidable accident" where you have to take some small damages to your car to avoid a much bigger accident.

Unfortunately, it can be difficult to track these people down after an incident.

But, if the accident was not your fault, and if you can get in contact with the person you consider to be responsible for the accident, it may be worth holding them responsible for your damages.

Determine Damages

Fortunately, single-car accidents tend to rack up smaller damages than multiple-car accidents. If you can walk away from an accident with nothing but a broken headlight and a bruised ego to show for it, there may not be any need to file.
But you need to be realistic and honest about this, especially where your health is concerned. If an auto insurance claim could cover the neck injury you sustained in the accident, or if your car is going to require some substantial repairs, it would be foolish to avoid treatment or repairs just because you don't want your premiums raised.

And of course, if you've damaged someone else's property, it's better to get in touch with them and give them your car insurance information now than it is to force them to track you down.
If you're lucky, you can brush a single-car accident off like it never happened. But be honest with yourself about just how lucky you were.