Wine should always be stored in a cool, temperature controlled environment, away from sunlight. With the advent of whole home air conditioning, anywhere inside your home is acceptable, as long as sunlight never directly hits the bottles.
Boxed Wines, Screw top bottles
The tradition of laying a bottle of wine on its' side isn't necessary with boxed wines and screw top bottles.
Traditional Corked Bottles
Wine sealed with a cork that will be stored long term needs to be lying on its' side, ensuring the wine inside touches the cork. Keeping the cork moist on the inside is vital to its' integrity. Corks are a natural wood and will dry out over time, possibly losing the seal, exposing the wine to bacteria and other contaminates, thus destroying the wine. It is also extremely difficult to remove dry corks from bottles, as they will crumble under any type of pressure.