I forgot to say once again, there have been many covers that have been covered. But the two that still remain the most sung is
HALLELUJAH by Leonard Cohen, I am so tired of hearing this song, no matter how well it is sang lol seriously...
And ALL OF ME by John Legend... I am like... stop, give "all of yourself" to someone else in another competition lol
I am sure there are a few floating around in my mind what I hear often now, but when I think of them, I will let you know. But yeah, try picking some songs no one has covered, there are so many out there that are amazing.
But at the end of the day, if you do an original, then it is a guarantee I have never heard it before if it is truly an original :)