Does donating sperm to a woman who is not your wife (who then goes on to bear children from it) fulfill the mitzvah of p'ru ur'vu?
Alternatively, is it a violation of halakha? Does it matter whose the egg is?
I heard a talk from Rabbi Barry Freundel at a medical ethics conference several years ago. The mitzva per se of pru urvu means: "marry someone who is able to bear children, to the best of your knowledge, and go about normal married life." One of the Achronim (sorry don't recall offhand) specifically writes he's not sure if one fulfills pru urvu if one's haploid cells wound up in a bathtub and then impregnated a woman who subsequently bathed there. I'm sure that case sounded crazy to most listeners then -- but today we call it artificial insemination.
You're discussing donating; receiving from a sperm bank is a different question.
There are almost always halachic issues with harvesting sperm (which raises the halachic problems -- I can see no reason donating to the bank beyond that should be problematic), yet I've read of sperm banks in Israel where rabbis have allowed it. CYLOR.
One could begin to argue in terms of halachic values (not the absolute commandment of "pru urvu"), such as "the world was made to be inhabited", or "think how this could help a childless couple", or the like; but I've never heard anyone say that anything depends on the recipient.