Forget the lips and the teeth. It's all about Jon's ass!
But to answer the original question, my favorite videos are Lay Your Hands On Me and Keep the Faith.
My least favorite is probably Thank You For Loving Me. I remember - before I was a fan or knew anything about Bon Jovi - seeing the It's My Life video and thinking "Wow they're pretty cool." Then when TYFLM came out I thought "WHAT HAPPENED??"
And yeah, the dog version of Who Says is just horrible.