rhotacism n.

eighteenth letter of the English alphabet, traceable to Phoenician and always representing more or less the same sound, which in many languages is typically so resonant and continuous as to be nearly akin to the vowels, but in English is closer to -l-.

It was aspirated at the start of words (hr-) in Old English, as in Greek, but this was abandoned in English spelling and pronunciation by the end of the Old English period, but the rh- spelling survives in many words borrowed from Greek. In many languages and some dialects (e.g. Scottish) it is pronounced with a distinct trilling vibration of the tongue-tip, which gave it its ancient nickname of "the dog letter;" in other regional dialects (e.g. Boston) it is omitted unless followed by a vowel, while in others it is introduced artificially in pronunciation ("idear," "drawring").

If all our r's that are written are pronounced, the sound is more common than any other in English utterance (over seven per cent.); the instances of occurrence before a vowel, and so of universal pronunciation, are only half as frequent. There are localities where the normal vibration of the tip of the tongue is replaced by one of the uvula, making a guttural trill, which is still more entitled to the name of "dog's letter" than is the ordinary r; such are considerable parts of France and Germany; the sound appears to occur only sporadically in English pronunciation. [Century Dictionary] 

Louise Pound ("The Humorous 'R'") notes that in British humorous writing, -ar- "popularly indicates the sound of the vowel in father" and formations like larf (for laugh) "are to be read with the broad vowel but no uttered r."

The moment we encounter the added r's of purp or dorg in our reading we know that we have to do with humor, and so with school-marm. The added consonants are supposed to be spoken, if the words are uttered, but, as a matter of fact, they are less often uttered than seen. The words are, indeed, largely visual forms; the humor is chiefly for the eye. [Louise Pound, "The Humorous 'R,'" American Mercury, October 1924]

She also quotes Henry James on the characteristic prominence of the medial -r- sound (which tends to be dropped in England and New England) in the speech of the U.S. Midwest, "under some strange impulse received toward consonantal recovery of balance, making it present even in words from which it is absent, bringing it in everywhere as with the small vulgar effect of a sort of morose grinding of the back teeth."

 In a circle, meaning "registered (trademark)," attested by 1925. R&R "rest and relaxation," is attested by 1953, American English; R&B "rhythm and blues" (type of popular music) is attested by 1949, American English. Form three Rs, see Three Rs.