Temperature can negatively affect the taste of wine, particularly rapid changes. In addition, some wine experts suggest that low humidity can cause corks to dry out. Exposure to sunlight is also something that can lessen the taste of a fine wine.
Wine collectors, generally speaking, mention 55°F as a perfect wine storage temperature. They add, however, that any wine temperature between 45°F and 65°F will likely be fine. Keeping relative humidity above 50% should be adequate to protect cork, most agree, but be careful to not keep humidity so high that you'll be in danger of attracting mold. Use a humidifier to increase humidity or a dehumidifier to decrease humidity. Rapid changes in conditions are the main thing to worry about, so always strive to keep your wines in a stable environment. Lastly, don't store wine where it can be exposed to direct sunlight. If storing expensive wines, particularly for long periods of time, definitely do your research to achieve proper “cellar” conditions.