I´m an alcoholic cocaine addict & a bartender/clubowner, so I´m quite often confronted with that question....
If invited for a shot, I just say I´ll have cherry juice (astonishing enough, this works & people still like me joining "Cheers" rounds). If invited for a drink, I just say what I want, that is usually tonic, orange juice, etc. Normal alcohol drinkers usually tend to drink unalcoholic drinks in between alcoholic drinks, so I really need to explain nothing if I do not want to.
If invited for a line, I just say I do not do or I do not have to do that anymore (That depends on who is asking)... But those questions reduced to being asked very seldom by now.
Some of my closest folk at work know about me. They know I am a cocaine addict & therefore stopped drinking in consequence, too. As those people mostly are active addicts in denial, well you can imagine that they are NOT comfortable with my not drinking/not using - I stoppped talking about my addiction nearly completely & only try to show by how I am & how I act that there is another way.
When people insist "Well, you can have one!!!!" I tell them that I do not drink anymore. And to my surprise a lot of them just say that is great & don´t question it. A couple have this "I try to cut down, too" attitudes, but that is about them & if my message makes them think about their own drinking patterns - well, that´s not bad, either....