I sold a car that I was still making payments on a couple of years ago. It's not impossible, but it is awkward. You need to find a patient buyer who really wants the car. If you're making payments, I assume the car is still a nice one, so:
1. Get it thoroughly detailed so it looks new (worth every penny);
2. Sell the car, using release-of-interest forms or whatever your state requires in lieu of a title;
3. Use the money to pay off the loan immediately (no using the money for a nice bike!);
4. Mail the title to the new owner when you get it.
You'll need to find a buyer who really trusts you to pull this off, so make sure you're trustworty, I guess. Of course, if you owe more than the car is now worth, you'll just have to suck it up and pay out of pocket, or be willing to take a 5-year hit to your credit. You might also have to sell the car for a bit less than it's worth just to get rid of it. In my case, I sold the truck for $1000 less than the blue book value, but I save at least $4000 a year by not having a car, so whatever you do to get rid of it will be well worth it, even from a limited, financial point of view. And then there are all those other, intangible benefits as well.