Q. Do people who cook boiled eggs today still accustom to boil at least three at the time?
A. Most Poskim espouse the view that blood in an egg that is the result of the fertilization process is biblically prohibited (Tur and Shulchan Oruch Yoreh Deah 66:1,2).
The reason for the tradition of boiling a minimum of three eggs together, is that in case one of them contains blood that prohibited egg will become nullified in the kosher majority created by the other two eggs.(see Toras Hamishpocho p. 76, as to how to remove the eggs from the pot when cooked)
Commercially available eggs today are generally unfertilized, as hens are segregated in huge coops and are not in contact with males. Such eggs are referred to in the Talmud as Safno Mearo and the blood found in such eggs does not prohibit the entire egg; only the blood spots themselves have to be removed.
Igrois Moshe, (Y. D. 1: 36) discusses the state of blood spotted eggs in countries where Safno Mearo eggs predominate and notes that the Minhag is still to discard the entire egg.
Yabia Omer (Y. D. 3:2) writes that the custom is to simply remove the blood spot and eat the rest of the egg (see similar position in Minchat Yitzchak 1:106 and 4:56:3)
It has been suggested that the reality has changed considerably since the writing of the Igrois Moishe response, and today it is highly unlikely that a fertilized egg will be sold as a table egg. As such there may not be anymore a reason to boil three eggs together.
Horav Shlomo Miller's Shlit"a position is that if one already observes this Minhag he should maintain it, as people do travel to different places and situations could change.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit"a
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