The OP was asking for non-alcoholic options. Thusly the other responses of a non-alcoholic nature.
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nevermind i read without as with
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I'm an IBC kinda guy. :-)
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I am enjoying a good quality coffee even more than I would my red wine or single malt right now.
Of course I also smoke in the morning on the weekend mostly and feel a little weird breaking out the bottle at 8am. I know...weird right?
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I drink sweet tea for non-alcoholic. I will definitely try those other 3.
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Ironbeer is one of my favorites, not sure how widely available it is though.
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Ok this may sound crazy but.... Milk... Try it and you might just find you love it. It can open up a huge number of flavors in the cigar that you never knew were there.
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I'm on board with everyone else with recommending:
AW Root Beer, only AW for me.
Coca Cola
Coffee

I'll also drink Water sometimes, nice change up since I try to avoid drinking a lot of Coke.
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Fixed it for ya'. dang PG censor. Think kitty cat.

I like MUG brand rootbeer and cream soda. Henry's makes a good product too.
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In the latest Ca interview with Brad Paisley he doesn't drink either and he says he likes to pair his smokes with Yoo Hoo and Grape Juice, I have yet to try these, but I am going to try the grape juice tonight maybe, will let you know.
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As some others have mentioned: Pellegrino, Lemon Pellegrino, Coke, coffee.

The Pellegrino leaves your palate feeling crisp and refreshed and the carbonation makes for a more interesting mouth feel

The Limonata (Lemon Pellegrino) and Coke have citric acid that refresh the palate

Coffee goes great with cigars, as the flavors compliment each other... the stronger the cigar, the stronger the coffee.

Several guys have mentioned rootbeer, but I havent had an opportunity to pair it with a cigar yet.
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+1 :-)
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In order of favorites:

Coffee (Always a home run)
Cream Soda (Sometimes it is too sweet for cetain smokes, othertimes amazing)
Water (Great for hydration and leaves you able to taste the pure cigar)
Coke (Works well with some smokes)
Birch Beer (Works well with some smokes)
Root Beer (I find it can bitter certain smokes)
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some of us work nights, so 8am is our 5 o'clock.

i have yet to try cream soda, but i have heard a lot about it. I have tried Pelligrino and enjoyed it.
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If you are smoking something creamy it will elevate it. I can't drink cream soda without a cigar now.
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Root Beer, Dr. Pepper, and Gingerale are my favorites. As far as Root Beer goes, I usually like something with a bit of bite in general, but I'm actually finding a creamier Root Beer with more vanilla goes better when smoking.

On the alcoholic front, I had a very pleasing smoke with a strange drink just the other night. A friend of mine received a bottle of Three Olive Loopey (fruit-loop flavored Vodka) as a gift, so we started experimenting and came up with the "Dirty Tucan", "Fruity Russian", or some other made up name consisting of the Loopey vodka, creme de minth (the only non-coffee cream liquor we had), and half-and-half with a few fruit loops on top to garnish... it was like Saturday Morning cartoons with booze! Also, strangely, a nice compliment to the Factory Throwout No. 59 Sweets we were smoking that night.
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:-):-):-)
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This board is the best. Thanks again for all the responses, I have many beverages to try. The three that pique my interest the most are cream soda, dr. pepper, and pellegrino.
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Cream soda FTW.
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What's the best tasting Root Beer out there?
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