When I first got into cigars I was a bit too young for the "adult" beverages, so I tended towards a good-quality still or sparkling water (Voss, San Pellegrino, Perrier) or club soda with a proper twist of lime. I usually preferred something that wouldn't mess with the taste of my smokes, as I smoked quite "seriously" back then (tasting notes, endless assessments of every element of each stick, etc).
Now that I'm older, I choose my beverages based on the cigar I'm smoking and the experience that I wish to have. If I'm doing a serious tasting, then I'll still go for clear, mostly tasteless beverages. If it's a so-so stick and I'm just smoking at home, then I'll either pour a nice blended scotch, an inexpensive red wine, or even a Diet Pepsi.
If I'm smoking some serious sticks at a cigar bar, or just to have a purely pleasurable expereience at home, then I break out the single-malt 21yr old Balvenie or at least mix a good Rusty Nail.
I do find that I try to keep my best cigars and wines separate, however. If I'm enjoying a particularly expensive/rare/exquisite stick or a bottle of my favorite vino (Caymus Cab, Cakebread Merlot, or Bollinger champagne), then I try to keep it non-competitive: great cigars get a clear tasteless beverage or possibly a good, mild spirit and my good wines and spirits are either tasted with bottle of Voss still water or drank with a properly chosen meal (preferably French or Modern American Fusion).
