Isn't C E A D G the time-honored "Circle of Fifths"? That's old enough and common enough for me to consider it an element of "folk" music.

F# also has a place in the key of E. I play the Smokey Robinson classic "Shop Around" in E with four chords: E/E7 and A (alternating, for much of each verse), then an F# to B7 before resolving back to the E.

(The F# comes on the line "My momma told ME." The B7 accopanies "you better" and back to the tonic E for "shop around.")