The convention of naming storms is a recent one. The earliest examples were destructive storms in the West Indies that made landfall on a particular saint's day, and were given the name of that saint.
The first recorded instance of such nomenclature was Hurricane Santa Ana, which struck Puerto Rico in July 1825. In the early 20th century the United States used a similar convention, but included both secular and religious holidays. Perhaps the most famous example was the catastrophic "Labor Day Hurricane," which struck the Florida Keys on September 2 and 3, 1935, causing hundreds of deaths and ending Henry Flagler's dream of building a railroad to Key West.
The first formalized system of naming storms was created near the end of the 19th century by Australian meteorologist Clement Wragge, who started naming storms after letters of the Greek alphabet. Later he changed to using the names from Greek and Roman mythology, and later still to common feminine names. U.S. military meteorologists picked up the convention during World War II, but at the end of the war, the system that became formalized was one which used the military's phonetic alphabet (Able, Baker, Charlie, etc.). In 1953 the Weather Service switched over to feminine names; the very first was Tropical Storm Alice. In 1978, due to sexist overtones (male meteorologists referring to the stormy personalities of women they knew), male names began alternating with female ones in the Eastern North Pacific, and in 1979 the practice was extended to the Atlantic and Gulf of Mexico region.
In that region there are six separate lists of names running from A through W, excluding the letters Q, U, X, Y and Z (names beginning with those letters are fewer and not as commonplace, and the intent is for names to be familiar and easy to remember). If the 21 remaining names are used up -- as happened in the 2005 season -- forecasters resort to the Greek alphabet. Every seventh year, the six lists repeat, so that Alberto, the name given to this year's first tropical storm, will appear again at the top of the list in 2012. Particularly costly or destructive storms have their names retired from the lists (Dennis, Katrina, Rita, Stan and Wilma were retired in 2005).
In addition to the Atlantic and Eastern North Pacific regions, there are regional lists for seven other regions of the world subject to tropical cyclones. Each list uses names common to the culture and language of local indigenous peoples to its region.