While driving without a license is a crime, there are many valid reasons a person without a license might want to buy a car. Teenagers who have been saving but who have not yet gotten a license may want to have their car ready as soon as they pass their driver's test. Family members who no longer drive might purchase cars for other family members. You can generally buy a car without a license, but you might have to jump through a few additional hoops.
TL;DR (Too Long; Didn't Read)
If you do not have a driver's license, you can often still purchase a car as long as you can meet the seller's requirements, which may include having another form of state identification and showing proof of your income. It can be more difficult, however, if you have had your license revoked or suspended.
Unless you're paying in cash and don't need financing, you'll usually need a photo identification to prove your identity. For most people, this identification is a license, and if you don't have one, you may have more difficulty proving who you are. Consider getting a state-issued photo identification card so that you can easily document your identity. This ID also proves your address and makes it easier for dealerships to get the information about you they need to approve you for financing.
Previous Driving Problems
If you don't have a license because it's been suspended, you may have more difficulty buying a car. Particularly if the dealership is financing your car, it may refuse to sell to someone with a suspended license. This is because people who have already lost a license, and who are given a car, may drive the car anyway and end up in jail, limiting their ability to repay the loan.
Purchasing a car and financing a car are actually two separate transactions. While it's perfectly legal to purchase a car without a license, dealerships can set their own requirements for financing, so long as these requirements are not discriminatory and don't violate any laws. Some dealerships may refuse to finance a car for a person without a license or require that people without licenses demonstrate that their licenses have not been suspended. You may also need to provide additional paperwork to prove your identity and income.
Taking the Car
When you purchase the car, the dealership won't allow you to drive it off of the lot if you don't have a license. However, if you have a learner's permit and a licensed driver with you, you will be able to drive it. Plan on taking a licensed driver to the dealership with you on the day you want to take the car home. Depending on state requirements, you also may not be able to insure or register your car if you don't have a license.