According to Wikipedia as well as my own experiences interacting with people of different nationalities, the pronunciation of 'Z' seems to have maintained some variation of the hard t- sound from the original Greek/Latin "zeta" in most Latin and Germanic languages. The only exceptions I can find are Portugese and American English. In the US, the "zee" pronunciation is so much the unanimous choice, I only recently became aware of this particularly slight against Her Majesty's alphabet.
According to Wikipedia, the 'zee' pronunciation comes "from a late 17th-century English dialectal form," citing a book by Thomas Lye from that period. So, is it fair to assume that this style was popular in England at the time and that American colonists, wanting to keep in vogue with the latest fashions out of the old country took it up?
The Canadian Encyclopedia offers the opposite explanation--that it was popularized in the spirit of the American Revolution to inspire rebellion against tyrannical taxation and spelling mandates. Another possibility is that it comes from the Alphabet Song, itself an American variation on a long-standing European tradition. (Zee rhymes with me but zed only rhymes with...Ted?) I think this was around the same time we invented football.
Personally, I think the ABC song was probably the most important contributor since it helped so many children learn to read and literacy was considered a valuable skill at that time. Would be interested to hear what others think. Any other possibilities that should be explored?