In Massachusetts, a title is required, however I purchased a car without a title. I had the police come to my house, they checked the serial number, and provided me a document to go with my bill of sale, to bring with me to the DMV.
The DMV collected sales tax based on a table the state has, not the bill of sale value, or whichever value is higher.
My title came in the mail in about 4 weeks.
Every state is different. You have to check with your local police and DMV.
Good Luck;