Jazzers sometimes use progressions from well-known tunes and name them by the tunes ("Rhythm" for "I Got Rhythm" was named above). Some folk players do as well -- "Don't Let Your Deal Go Down" (or "Salty Dog" or 1000 other songs) is pretty common. I usually call that one the "Circle of Fifths" when I refer to it --
in G, for instance, it's G / E7 / A7 / D7 / G, and each chord is followed by the one it's the fifth note of, except the first change (to E7). It could easily be called the "Circle of Fourths" if you're counting forwards, but for some reason, we don't call it that.
The typical progression of I/IV/I/V7/I (in G, again, that's G/C/G/D7/G) doesn't have a name to my knowledge. It's used in a jillion songs, from "This Land Is Your Land" to "When the World's On Fire" (hidden trivia quiz -- why do I use those tunes as examples?).
The "Blue Moon" progression mentioned above (G / Em / C / G7 ...) is also common (1950s rock wouldn't have existed without it).
But naming progressions isn't terribly common in folk, it seems.