No annual stickers here in Tennessee. Once you are granted an Antique plate...it's good for as long as you own the car. Any subsequent owner must reapply for the antique status, though. I live in the county, too, so no city inspection either.
Also...the law says you must only drive an antique car to "...club meetings, shows, parades, or for mechanical repair purposes..."...or words to that effect. You're not "supposed" to use antiques for daily transportation. I've never been stopped and I drive "Jippy" to work all the time. Just to be safe, however, I always carry a small piece of radiator hose with me and should I get pulled over...
"Officer, I was on my way to the parts store to match this piece of radiator hose! Honest, I was...!"