Only at the start of words, and in certain other positions in a word. Not necessary in the word "letter", for example, which you hear as "lettah" or "letta". In many things, Americans are more laid back than Brits and Australians, but they are sticklerrrrs for pronouncing every arrrrr. (Actually, I'm not sure this is consistent across all states. I'm guessing it isn't.)
In one of Alfred Hitchcock's early movies, Secret Agent (1936), John Gielgud is told by the head of the Secret Service, "You can call me Ah." Gielgud asks, "Ah exclamation?" The head of the Secret Service says, "No, Ah as in rhododendron."
