Oxygen is the worst enemy to the actual wine inside the bottle. The bottles are sealed from the oxygen with pliable, expansive cork. If the cork dries out, it will shrink and possibly let oxygen enter the bottle and oxidize the wine.
Storing the wine on its side will keep the cork moist and maintain the air tight seal for a good deal of time. For extreme periods of time, a humidity controlled environment will be needed to keep the cork from drying out.