We're talking favorite obscure show tunes here, and I can go back a long ways:
Jane, Jane, Jane (1903, BABES IN TOYLAND)
Jack-o-lantern Love (1912, LADY OF THE SLIPPER)
The Sun Shines Brighter (1917, LEAVE IT TO JANE)
Not Yet (1917, OH, LADY! LADY!)
Once in a Blue Moon (1923, STEPPING STONES)
Where The Hudson River Flows (1925, DEAREST ENEMY)
New York Serenade (1928, ROSALIE)
Starting at the Bottom (1930, FINE AND DANDY)
Ballad of the Robbers (1938, KNICKERBOCKER HOLIDAY)
Every Sunday Afternoon (1940, HIGHER AND HIGHER)
Nickel for a Dime (1940, TAN MANHATTAN)
Here I'll Stay (1948, LOVE LIFE)
Stay Well (1949, LOST IN THE STARS)
The advent of long play recordings and original cast albums in America covered a lot of ground in the 1940s to today, so I don't know what's obscure any more. I can think of a few, not-released-on-CD off-Broadway shows from the 1960s that have some great obscure numbers:
A More Than Ordinary Glorious Vocabulary (1961, ALL IN LOVE)
A Man With a Load of Mischief (1966, MAN WITH A LOAD OF MISCHIEF)
I Want to Walk to San Francisco (1969, THE LAST SWEET DAYS OF ISAAC)
And there I'll stop.