This is probably the original, of which the others mentioned above are parodies:

Copied from http://www.ladyday.net/song/song171.html

MY OLD FLAME
(Arthur Johnson / Sam Coslow)

My old flame
I can't even think of his name
But it's funny now and then
How my thoughts go flashing back again
To my old flame

My old flame
My new lovers all seem so tame
For I haven't met a gent
So innocent or elegant
As my old flame

I've met so many men
With fascinating ways
A fascinating gaze in their eyes
Some who sent me up to the skies
But their attempts at love
Were only imitations of
My old flame
I can't even think of his name
But I'll never be the same
Until I discover what became
Of my old flame

[AMG/All Music Guide lists 358 recordings of this song. Billie Holiday's was an early one, if not the first.]