You say Myanmar, I say...
I've been thinking about saying something about the pronunciation of Burma/Myanmar, since the name has been mentioned in several media reports following Cyclone Nargis. Maybe I should just point.
According to Wikipedia, in Burmese the country's name is (pjìdàunzṵ mjəmà nàinŋàndɔ̀), but contributors disagree on the proper English name.
Phonetician John Wells discussed the British and American pronunciations, and their relationship to Burmese politics, back on 11 October 2007.
In Burmese, this name Myanmar is essentially just a variant of the name Burma. It is transliterated as Myan-ma or Mran-ma, and in the local language pronounced something like [ma(n) ma], as against [ba ma] for the traditional name.
Language Log has an updated discussion today, which quotes a BBC News Magazine piece from last fall.
Bottom line: The government seems to prefer the spelling <Myanmar>, while the opposition prefers <Burma>, but in terms of pronunciation, neither word has an American R sound. It is [mjən ma] or [bə ma], not [mi æn mar] or [bɝ mə].