My dad is a recovering alcoholic (been sober for about 20 years now, I think), and if he's pressed he usually says that he's allergic to alcohol. It makes him dizzy, uncoordinated, and give him a big headache the next day. Of course, this is the normal reaction that human beings have to alcohol, but only some people (especially if they are already drunk) catch that.
I'm usually truthful when pressed. I claim alcoholism in my family, and that I was headed in the same direction as my father when I did drink, so I don't anymore. And, as other people have said, I always volunteer to be the designated driver whenever we go anywhere that serves alcohol. Most of my friends are more than happy to let me drive so they don't have to worry about what they drink.
I think, as others have said, that just not making a big deal out of it is probably the best way to go when going out with people you don't know well. If they ask you about it then you could just say something like, "I don't drink, but I'm okay with other people drinking." I think a lot of the time people feel uncomfortable drinking around somebody who doesn't drink because they feel the non-drinker is judging them, like they're a Sunday School teacher or something. If you say right out front that you don't have a problem with drinking in general they'll be more inclined to take, "I don't drink," as an answer.