Can't get much more obsequious than Gone Gone Gone.
From the last verse: If I knew where I could find her, I'd crawl there on my hands and knees...

And the ultimate (female) grovelling song by Cole Porter: [SO IN LOVE]

So beat me and hurt me,
Deceive me, desert me,
I'm yours 'til I die.
So in love, so in love,
With you am I.