Libertarians do not believe that drunk driving should be illegal.
Read that one again.
I hate this one because there's no possible way to hear it for the first time and think the speaker has all his marbles. I suspect that some will retain that thought regardless of my explanation to follow. However, more than any other issue that libertarians espouse, I believe this one causes most people anguish, and deserves explanation.
Imagine this scenario: A man is in a bar, and has had a few too many. Maybe just one too many, but still, it's too much. He stumbles out to his car, miraculously finds the right key, argues with the door handle for a few seconds, then flops into the driver's position. After seven or eight attempts and a couple of hiccuping giggles, he manages to get the car started, puts it into drive via muscle memory, and drives home. During the trip, he violates no traffic laws, and arrives home safely without incident. He staggers inside his house, and falls asleep.
In this scenario, a crime has been committed. Depending on how many times the man has engaged in this behavior, it is possible he just committed a felony. In most jurisdictions, regardless of his history, he would be guaranteed of jail time, community service, a fine, and a host of other legal troubles.
The libertarian problem with this punishment is that no person was actually injured in any way. Much like Pre-Crime in the movie Minority Report, punishments for this crime are derived from the notion of what might have happened, rather than what did. The fact that he was impaired had no effect on the outside world, and yet, a curious or bored police officer stop would've guaranteed the man go to jail, leads many libertarians, including myself, to call drunk driving laws unjust.
Now...the question in your mind is what I want to do with drunks who crash into people. Three words: HANG. THEM. HIGH. I have no problem with drunkenness being a mitigating factor in these sorts of incidents, and in fact, would argue that a crash incurred due to drunkenness indicates a wanton disregard for human life. Throw the book at them. Lock them up forever. I would even be inclined to call a vehicular homicide where alcohol played a factor murder.
So...from the Friendly Libertarian...I say drink up, but know your limits. This is one dice game in which you don't want to crap out.