I quit alcohol a few years ago. I wasn't an alcoholic or anything of the sort --- I just decided to stop.
For social things along the lines of house parties, I'll bring my own cup. I bought a set of vintage tupperware cups, and, to my surprise, they're always a hit. Its silly, but it helps. I don't make a show of drinking water, and most people assume the cup is filled with beer. When people do ask what I'm drinking, and I tell them that its just water, my assumption is that their assumption is that I was / am an alcoholic... sometimes I let it slide, other times I will clarify.
Over these past few years I've moved away from everything but one cup of coffee per day, and about 2 - 3 litres of water.
Regarding the stigma, it may be a regional thing (Vancouver), but most people don't care about what I order at a restaurant or drink at a social function. The strangest look I'll get is when I order room temperature tap water... but that's understandable :)
Since moving away from everything else, I've found that I rarely crave sugar --- and when I do, everything is far too sweet for me. I used to have a notorious sweet-tooth, but moving away has cured me of that. I also can't handle fizzy things anymore, which was also surprising.