The Zyliss Wine and Champagne Keeper is worth a mention. It seals the bottle and either removes the air (best for still wine) or adds pressure (for the bubbly).
I’m not a big fan of those; for champagne, the simple pressure stoppers that were linked above do fine.
For wine, the best way to keep it that I’ve found is to put the cork back in and put it in the fridge. Keeping it cold is the real trick to keeping it fresh; pumping the air out doesn’t make much of a difference in my experience.
My Dad always used to insist that suspending a tea spoon in the neck of the bottle and leaving it there until you’re ready to drink the rest of the bottle prevented the champagne going flat.
It didn’t work, of course, but the habit alone is an interesting piece of social anthropology.