The best temperature for storing all wines – reds, whites, champagnes, and ports – is around 55 degrees (F). For long-term storage – 6 months or more – you really want to stay around this temperature. For short-term storage, the temperature doesn't matter as much. In fact, you can just store it at room temperature (typically around 72 degrees F). Much above that temperature, your wine will age rapidly, and possibly be ruined completely.
You'll definitely need to keep it away from heat sources at all times (hint: don't store it in a wine rack on the kitchen counter). Even a day at very high temperature, say in the trunk of your car, can “cook” a wine, making it undrinkable, so always avoid higher temperatures when possible.
Many casual wine drinkers are aware of the problems with heat in wine storage, and some may opt to store their wine in the kitchen fridge. However, this is not a good practice, for a number of reasons. First, the temperature is actually too cold, and if left there long-term, can actually “flatten” the taste of the wine. Also, the air in the fridge is too dry, and will dry out the cork. Finally, strong odors from food like onions and garlic in the fridge can infiltrate the wine – giving it a rather nasty off-taste. If you need to store your wine for more than a few months, your better off investing in a small wine fridge/wine cooler – a special refrigerator that maintains the temperature at the ideal level, and (typically) controls humidity as well.
In addition to temperature concerns, for longer term storage, you'll want to pay attention to humidity, light exposure, and vibration. For more on these factors, see our article on the four enemies of wine.