For many speakers, including myself, "Mary", "merry", and "marry" are homonyms: meɹi. For other speakers, including my father, there is a threeway difference reflecting the underlying forms: me(j)ɹi, 'Mary', mɛɹi, 'merry', mæɹi, 'marry'. Generally, the distinctive forms belong to non-rhotic dialects, and the neutralized forms to rhotic dialects. This is because in rhotic dialects, intervocalic resonants tend to be ambisyllabic, i.e., they are attached both to the syllable that precedes them (as a coda) and the syllable that follows them (as an onset). An /r/ in coda position tends to neutralize many if not all vowel quality distinctions in the syllable it closes, and thus in rhotic dialects, where these syllables are closed by an /r/, we get all three front vowels neutralized to the [-hi][-lo][+ATR] vowel /e/. For non-rhotic speakers, /r/ can never be in coda position, and thus this neutralization does not occur.
Because of this, rhotic speakers tend not to be able to identify which form is which, even on hearing them produced by non-rhotic speakers (or rhotic speakers who happened to have picked up the distinction in careful speech). I occupy some sort of no man's land in between, since I understand the distinction, and can produce it, but I never use it in normal speech. I probably inherited this from my father, who, while a rhotic speaker, comes from family in New York, and probably heard many non-rhotic speakers (in addition to being a careful and conservative speaker himself). I recently encountered this difficulty on two fronts.
The first was in the TV show "Frasier". The character Niles, a rhotic but very careful speaker, played by David Hyde Pierce, also a rhotic speaker is discussing some former patients with commitment issues who overcame their disorder and were getting mɛɹid, which for a non-rhotic speaker would be "merried". This error seems a bit odd to me, since Pierce was born and raised in New York, was a camp counselour in New Hampshire, and went to school in Connecticut, so he surely was exposed to non-rhotic accents throughout his life. However, if he never acquired the distinction, it would be exceedingly difficult for him to recreate it. Though he didn't make the distinction, he knew that Niles likely would, and thus made a guess at one of the forms.
The second was my wife Amanda, discussing a coworker, with a New Jersey accent, who wished her a mæɹi Christmas. What the coworker actually said was almost certainly mɛɹi, but to a rhotic speaker like Amanda there is little, if any, perceivable difference between to two.