Mick Jagger sang "Ain't too Proud to Beg", but I don't know if he ever sang "My Girl" or "Just My Imagination".
I have never really been a Stones fan either, but there is one song by them that I really love. The name of it is "Till the Next Goodbye". They even mention Louisiana in this song :-) See if you like it.
I like "Working My Way Back to You" by the Spinners. I like "Could it be I'm Falling in Love" even better.
I think my favorite Spinners song is, "It's a Shame". Do you like that one?
I agree that great songs do make you forget everything else for awhile :-)