The Station Restaurant in Ithaca has one (real thing, I believe) along side its dining car

He who drives
When he's been drinking
Counts on you
To do his thinking
Burma Shave

One I remember from my youth

Free, free
A trip to Mars
For 900
Empty jars
Burma Shave

The first person to collect 900 empty Burma Shave jars and send them in got a free trip to Mars (Marz?), Germany.

There's a book, The Verse by the Side of the Road that not only lists the entire run but relates the story. They used to get local farmers to mount and care for the signs, keeping them clean and painted.