Yeats's "The Song of the Wandering Aengus" is somewhat more commonly known in song form as "The Golden Apples of the Sun".

Longfellow's "Song of Life" is in Common Meter, so it's been set more than once. A short discussion here.

John Greenleaf Whittier's "The Song of the Vermonters, 1799" has appeared in tradition with more than one tune. (It's in Helen Hartness Flanders's "New Green Mountain Songster"; I learned it from with a different tune.)

Margaret MacArthur set lots of Vermont poems to music, but they're not what you'd call "common" poems. See here, for example.

~ Becky in Tucson