I love to see Bon Jovi perform songs that aren't theirs; I.E Meatloafs "Love Hurts", Bob Dylans "Knocking on Heavens Door", and more.
I always dream of what songs Bon Jovi would kick the ass of if they did a cover for the song. Heres my list:
1) Unchained Melody (Righteous Brothers)
2) Johnny B Goode (i heard they already done this.. haven't heard it though)
3) Rawhide
4) Please Forgive Me (Bryan Adams)
5) Stairway to Heaven (Led Zeppelin)
6) Shake your Tailfeathers (Ray Charles)
7) I can't stop loving you (Ray Charles)

Iris (Goo Goo Dolls)
9) Careless Whisper (Wham! And George Michael)
Those are just my thoughts; If i had more time i'd list more.
And your ideas?