It's not what you think.
Mount Gay is a dark rum produced in Barbados from fermented sugar cane. The origins of the name are innocent enough, but thanks to more recent connotations attributed to the words, you will rarely find a drunken college student shouting, "I climbed Mount Gay!" It is a tastier but more expensive alternative to the ubiquitous Bacardi and Captain Morgan's (unless, of course, you're in the islands, where Mount Gay is ridiculously cheap if you happen to be a tourist armed with American dollars.)
History
The genesis of Mount Gay can be traced back to 17th century Barbados, making it one of the oldest brands of rum in the world. The production of Mount Gay rum began sometime between 1663 and 1703 on a sugar plantation located on the slopes of Mount Gilboa. The tradition at the time was to name a plantation after the owner. Ironically, the owner was a man named John Sober, so the rum was originally produced on the Mount Sober plantation.
Sober and his son, like most Caribbean landowners during this time period, did not live or work on their land, but hired a proxy landlord to look after matters instead. They left their plantation in the hands of trusted family friend Sir John Gay Alleyne. After Alleyne's death, Sober's son rechristened the plantation as Mount Gay in his honor, for there was already a Mount Alleyne in the area.
Throughout the 18th and 19th centuries, the facilities for producing Mount Gay rum grew from a single still to a large distillery compound. The distribution of the rum remained almost exclusively local, limited to Barbados and neighboring islands. In the early 20th century, the Mount Gay estate was purchased by businessman Aubrey Ward, who introduced the rum to an international market. The Ward family continued to operate the distillery until 1989, when the French conglomerate Remy Cointreau Group purchased a majority interest in the company.
Taste
Mount Gay is relatively heavy bodied rum, a warm amber in color. The flavor is rich and mellow. At first taste, the rum has a spicy bite, but the aftertaste is fruity. You can use it in mixed drinks if you wish, but I've found that the taste of the rum does not always blend well with the other drink ingredients. Whatever you do, don't use Mount Gay in a rum and coke. The spicy sweetness of the rum combined with carbonated cola is, well, stomach turning. It's not particularly good as a shooter either, as the flavor can be overpowering if downed in a quick shot. Mount Gay is best enjoyed straight, slowly sipped at room temperature. The flavor also makes it uniquely suited for use in cooking sauces that require rum, but the price is rather high to waste it as a cooking liquor.
Availability
Mount Gay rum is available at liquor stores across the United States, as well as in areas of Europe (mostly in France, Germany, and Italy). It is more difficult to find in the Southern United States, undoubtedly because of its name, which discourages many potential drinkers. Unsurprisingly, I've heard that Mount Gay has become increasingly popular as a top shelf drink in local gay bars. I'm sure this phenomenon is not limited to Washington, D.C..
Sources:
http://www.ministryofrum.com
http://www.mountgayrum.com