Do they require titles on vintage motorcycles?

Example: 1973 Honda CL350 in Tennessee?

Depends on the state and their definition of 'vintage' or 'Antique'. Pre WW2 some states didn't have title - registration only- and the state laws weren't updated for requiring titles until 1970s when federal standards were 'suggested' and required for imports, interstate trade. New York State waited until about mid 1980's for cars, trucks. Some states got the cars and trucks but left out motorcycles for another legislative cycle in 1970s- wasn't until 1981 when cycle VIN standards established that the state just starting the process could handle the identification process and they grandfathered in older cycle with just registration at times- title not issued until transferred out of direct family - Illinois case in 1970s with riding buddy getting a 1929 Harley JD that had been ridden by uncle- the 1937 registration found in paperwork kept by estate was the start of it's title. A 1973 Honda likely had a title if it was road registered in Tennessee-- I did one deal with Tennessee paperwork on a 1958 Harley frame and got a title with it but title had been originated in late 1960s. 1980 Georgia scooter didn't have title- used the municipal tag and inspection in Iowa to get plates and title. Dirt and raceing cycles that didn't get a license plate rarely got titles from most states, still don't often unless it is financed. 1973 is not a 'antique'- might qualify as a 'Classic' - depends on the states license plate and inspection for equipment laws- brother 1939 Chevy sedan got on road legally for daylight use only, not allowed on interstate with the Antique' plate that by definition were for pre WW2 cars made before January 1942- and they weren't titled until they got on road with the 'Antique' plate as a option. Pre 1960 motorcycles of smaller size in a few states might not have been titled- note the previous Georgia- and Alabama paperwork on one 1950s project worked on in mid 1970's didn't come with title- the registration and bill of sale form on back of registration was the transfer method, proof of ownership- completion of inspection and tax to county court clerk got you new registration.

Of course.

Call the dmv and ask them