Interestingly, this question appeared as number 15 on the Harvard Dialect Survey, so it is possible to give a good summary of the pronunciation differences in these three words as they are spoken in the United States.
The 11,422 respondents were asked to choose from five options given the following prompt:
How do you pronounce Mary/merry/marry?
The percentages next to each choice indicate the proportion of survey participants that chose that option:
a. all 3 are the same (56.88%)
b. all 3 are different (17.34%)
c. Mary and merry are the same; marry is different (8.97%)
d. merry and marry are the same; Mary is different (0.96%)
e. Mary and marry are the same; merry is different (15.84%)
The maps that show where in the US the respondents for each answer choice were located are available here, but can be summarized by noting that mid-westerners (residents of Ohio, Illinois, etc.) seem most likely to pronounce all three the same, and New Englanders seem most likely to pronounce at least two of them differently.
As for non-US speakers, a linguistics blog post by Ryan Denzer-King claims that,
…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.
So it is more likely that you would hear people talk without these three sounds being merged into one in places outside of North America. This seems logical to me, but I don't know enough rhotic speakers to say if it matches my experience, and there will of course be exceptions everywhere.