The "What would Jesus do?" expression actually comes from the Christian Classic book entitled In His Steps, by Charles Sheldon. In this great novel, a group of believers look at 1 Peter 2:21 and, based on that teaching, ask the question, "What would Jesus do?"
To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps. 1 Peter 2:21 NIV
The story follows several of them as they try to truly live their own lives as they believe Jesus would. A newspaper editor, a wealthy lady, and a few younger people incur disdain from other Christians who suggest that living in such a way is not practical. It really is a pretty good book. I've both read it and listened to an audio book version of it occasionally.
Anyway, it seems that this question, which comes from a book written in 1897, recently became a fad, abbreviated in the initials of WWJD.
It is important to note that the only way anyone can hope to know what Jesus would do is to study what He did do. It seems that too often some have based their ideas about what Jesus would do on a concept of Jesus that has nothing to do with His actual life and teachings.