ANSWER
Rhoticism is a quality of certain English language accents, known as rhotic accents, where the "r" sound is pronounced everywhere it appears in the spelling of a word. In non-rhotic accents, the "r" sound is only pronounced if it is followed by a vowel.
All English accents can be classified as either rhotic or non-rhotic. Most of England speaks with a non-rhotic accent. This includes Received Pronunciation (RP), the preferred accent of the British upper class and the BBC. However in Ireland and Scotland, English is spoken with a rhotic accent.
In the US, most of the country speaks with a rhotic accent, including the generalized Midwestern accent of the American TV networks. However certain areas speak with a decidedly non-rhotic accent, particularly New England (think Baa-ston, Massachusetts) and the coastal Southeast (as in Cha-uh-lston, South Ca-uh-lina, or Savannah, Jaw-ga). In New York City, which has a number of distinct accents, one can find both rhotic and non-rhotic varieties.
At one time, in the days of Shakespeare and Queen Elizabeth I, all English was rhotic. The switch to a non-rhotic accent began in southeast England. It became associated with the well educated and the upper class, and as such it was perceived as being a more prestigious way to speak. Over the years it spread outward from there, at least to areas that held no cultural animosity towards the English. There was enough contact between England and port cities of America for it to spread to coastal areas, however inland areas were more isolated, both from England and the coastal cities, so their accents remained rhotic. Consequently, the English spoken today in London, Kentucky may be closer to Elizabethan English that the English spoken in London, England. New York City is unusual because it is one of the few places where the "prestigious" accent shifted from a non-rhotic back to a rhotic accent. The happened after World War II, most likely the result of a large influx of Midwesterners to the city.
One curious aspect of non-rhotic accents is the tendency for the "r" sound to reappear, sometimes in unexpected places. Since "r"s are only pronounced when followed by a vowel, "r"s at the end of words are not pronounced, unless the following word begins with a vowel, in which case they sometimes magically reappear. This same tendency causes "r"s to occasionally pop up at the end of words that never had an "r" in the first place. (All this goes to explain why my friend from Long Island liked to have a "soder" with her "pizzer".)
(However, none of this explains why the "t" and the "r" swap places in the pronunciation of the word "comfortable".)
(Honorable mention to Arne Haaning and Trish Boggs, for correctly describing "rhotacism".)
WHO GOT IT RIGHT: JP Weigt, Ryan Scannell, Kathi Reynolds, Michelle Lewis, Robert Walker, Christine Severen, Matthew Toups, Marc Quinlivan, Bob Milligan, Brian R Bement, and Brett Dougherty.
