This one's a traditional tune, whose origin is not very clear. Is it from Britain, Ireland, or is it an American creation ? Nobody knows for sure.
It was first published by WC Handy as "Loveless Love", and it is more common in blues and jazz than in country music.
My favourite version is by New Orleans guitar player Lonnie Johnson. I love his almost introspective singing.
Lonnie Johnson – Careless Love (buy) (New York, nov 1928)
There's also a great country version by The Delmore Brothers, one of the greatest harmonizing duets. Sort of musical grandfathers to Gary Louris & Mark Olson (fathers being the Everly Bros, of course).
Delmore Brothers – Careless Love (buy) (Chicago, jan 1938)