english: me, mine, my
Russian: мне, меня, мой
Estonian: mina, mind, mulle
How prevalent is this in world's languages and what should it be attributed to?
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According to WALS, no. 53 languages sampled have /m/ in the first person singular and 177 languages do not. More interestingly though, there are more than just the Indo-European languages (like all your examples) that have 1st person pronouns with /m/.
Expanding on kaleissin's answer, WALS further said that the /m/ sound for first person pronoun is common in northern Eurasia (regardless of language family) and rare elsewhere, and tend to co-occur with T-like consonant as second person pronouns (usually t, d, s).
Two theories have been discussed for the apparent regional universality
Nasal consonants (like m) are easy to pronounce, so they have higher probability to occur in basic words such as pronouns. However, this theory can't explain why "m" is dominant than other nasal sounds, why only first-person, and why m-based first-person pronouns tend to co-occur with t-based second-person pronouns. This also can't explain why it's only common in northern Eurasia.
They come from the same genealogical origin. However this combination appears in many language families, such as Indo-European, Turkic and Uralic (and they also have T-based second person pronoun).