The Grateful Dead have a song from their Anthem of the Sun album that was rarely performed live called "New Potato Caboose." "New Potato Caboose" is a composition by Phil Lesh, Grateful Dead bassist. In several performances of this song the band plays a very familiar sounding classical theme that Phil Lesh usually initiates. One prime example starts at 5:30 in the link provided. The band coalesces around this familiar bass line and Jerry expounds on this familiar tune at about 7:15 before bringing it back to "New Potato Caboose" around 7:30. I was hoping someone would be able to identify the song that is quoted here. After many years Grateful Dead scholars have yet to determine the origin of this elusive jam.
It's a very quick listen and after the first few notes I'm sure you will be singing the tune instinctively.
More info about the song and jam can be found here,