Most wine can be kept in the refrigerator overnight, some whites will be ok for a couple of days. They don't really go bad, but just don't taste as good.
The air vacuums Rod mentioned help increase the storage time a bit, though personnaly i rarely have to worry about keeping opened wine, it doesnt last that long.
If you do keep wine for the next day, you may want to pick up some plastic re-usable push in caps from a wine store. It's not always easy to get a cork back in. (make sure you wash them in very hot water to avoid any bacteria from spoiling the wine)
If you make your own wine, as I do, bottle some in smaller 375ml bottles for those times when only a half bottle might be needed.
hope this helps