While vinyl records that spin at 78 revolutions per minute stopped being made in 1960, enough of them still exist that they are too common to be worth much. In particular, 78 rpm records featuring big band music, opera, popular songs and classical music are fairly easy to find.
While the earliest 78 rpm records date back to the late 1800s, 78 rpm wasn't established as a standard speed until the 1920s. These records are typically 10 or 12 inches in diameter and have much coarser grooves than the "micro-groove" records designed to play at 45 or 33 rpm. Vinyl 78 record are typically easy to break due to their brittleness.