OK, I'll offer my opinion and see if this gets things started.  My pick would be "Drown In My Own Tears."  The song was written by Henry Glover way back in 1956, but it's been covered about 30 differnt times since then by various artists; the most notable being the Ray Charles version of the song. 

But, my favorite cover version of this song is the one recored by Johnny Winter around 1968 or '69.  The music is great on that version, with Johnny's brother Edgar playing both the sax and the piano track in the recording.  Every time it gets to the part where the lead singer says "Come on and cry...",  I just want to bust out with a mean blues lick on my guitar.

BTW, Johnny Winter provides the lead vocal in that version, but I prefer Ray Charles' voice.  What would really great (to me) would be if you could put Ray Charles voice in the Johhny Winter cover version.  But you can't have it all, I guess.  Ray's version is in the key of A and Johnny's version is in C.  Maybe Bruno Mars should record this song in the key of C and do the music just like the Johnny Winter version  Hot dang!  That would be great.  I can dream can't I?