Uff. This is always a hot debate. I personally do not drink them. What would my motive to drink one be other than to feel and look like I'm drinking alcohol? I can't think of one, and what it really comes down to at the end of the day is your motives.
Recently though, I ordered a non-alcoholic Bloody Mary at brunch with some sober friends. Someone else ordered one, so I figured it was an OK/safe thing to do. Took two sips and it immediately felt too much like drinking alcohol for me to handle. So, I put it down and don't see myself drinking a virgin Bloody Mary anywhere in the near future.
But that's my own plan/experience. Also, just a last thought-- NA beer does have a slight bit of alcohol in it. So keep that in mind.