The answer to this question for me is rum...but that's not surprising because rum is the answer to a lot of questions for me...
Pyrat XO Reserve and Diplomatico Reserva are two that I regularly drink while smoking.
EDIT: and, to stay on topic, they seem to clear the pallet quite well too.
Tea, strong, sweet and lots of it, especially with Latakia forward blends, for me something magical happens with that combination that no other beverage comes close to producing, rich, deep fruit flavors come through mixed with exotic spice notes, also tea quenches a thirst better than any other drink other than water that is! Pipe smoking and tea drinking, a combination made in heaven, it has to be good tea though Typhoo, Tetley, PG Tips or Yorkshire Tea I find to be the best.
I guess I'm weird for a good piece of strong, strong, STRONG peppermint gum after a smoke. Cleanses my palate towards the end of the piece. I really think it kicks loose a bit of flavor of the smoke that I didn't catch before. Also settles my tummy if I get a bit much nicotine in my system. I picked up that habit smoking cigars some years back, and it always made the smoke more enjoyable at the end.