A humid environment is necessary for the proper storage of all fine wines sealed by natural cork. Humidity helps maintain the elasticity of the cork seal by contributing to (or not diminishing) the natural cork moisture content of 5% to 7%. An excellent review of issues pertaining to wine corks and elasticity can be found here.

Excessive humidity will result in the development of mold. Mold can attack labels and render them unreadable. The visible presence of mold may also reduce the value of your collection. Several auction houses refuse moldy consignments, as they present a risk to their employees and clients alike. Mold on the exterior of corks can also impart off flavors to wine. To avoid the development of mold potentially harmful to human heath, the US
Center for Disease Control has recently revised recommendations that relative humidity in indoor environments not exceed 50 percent.

I follow the
CDC guidelines at The Wine Rack by David Gray, and at home, maintaining relative humidity at 50 percent.

At home, humidity increases can often be achieved with a simple bucket of clean water and rag as a wick, a small inexpensive decorative style water fountain, a dedicated portable humidifier or mister, or humidity control integrated into the cooling system. 35 percent relative humidity is considered to be the human “comfort zone”, but is too low for long term wine storage.

Keep in mind that cooling units without offsetting humidity systems will draw water out of the air (and a cork), and reduce the relative humidity of the cooled space.  Monitor your humidity, and supplement as required to maintain humidity at 50 percent. The greater your humidity set point, the more energy that will be required to maintain that set point.