I think that Bon Jovi would be much "bigger" and more respected band with the right singles.They've made some HUGE mistakes with latest singles and that's why they're not so popular(on tv,radio,press...)
I have no problem with 80's and 90's singles so I'll go just for this decade

Crush:
It's my life
One Wild Night
Thank You For Loving me
Say It Isn't So

Bounce:
Bounce!!!
Undivided!!!
Missunderstood
Everyday

HAND:
DIRTY LITTLE SECRET!!!
Have A Nice Day
Last Man Standing
NOTHING

LH:
Make A Memory
Any Other Day
Walk Like A Man

Circle:
Brokenpromiseland!!
Love's The Only Rule!!
We Weren't Born To Follow
Work For The Working Man

GH:
What Do You Got
This Is Love, This Is Life!!!
No Apologies