I've done this for nearly every job in the past. However, since moving to the Bay Area, I would never consider quitting my job just to look for another. As one commenter below said, you put yourself at a disadvantage when you're bargaining for compensation.

I can agree that it's pretty difficult to find a new job while still working. However, most companies let you work from home nowadays. You can just interview during that time. Is it ethical? Who cares? It's business; the nature of the beast.