Nope. Liability yes. Comprehensive no. The reason is twofold. One, if I get in a wreck and it's someone else's fault, their liability insurance should cover me. Two, and this one is probably more important, the insurance company won't pay much even if it is my fault. Remember, they aren't going to buy you a new car. They're going to pay just enough, assuming it's totaled, to get an equivalent used car. If you can go a year without crashing, that pays for a new used car right there with the money you saved on premiums. Did I mention I drive a cheap car?
This is only partly true.
If you are in a wreck and it's the other guy's fault, you have to worry about whether he is adequately insured or insured at all. Those are your underinsured and uninsured coverages.
Comprehensive also covers various losses besides a wreck. If your laptop is stolen from your $500 car it might be covered for example.
I did not carry anything but liability on my old beater pickup. But really, everyone should shop wisely and only cover the risks that you can't afford to cover on your own.