I say AY-zores, you say a-ZORZ.
And guess what: We're both wrong.
Well, maybe not completely wrong. After all, AY-zores is the preferred pronunciation in Webster's. The British put the accent on the second syllable, which is beginning to sound more natural to me. But the other day someone here suggested very gently that if I was going to go around telling people about my time in the Azores, I should start pronouncing it correctly. It has three syllables, as in the Portuguese (Açores): a-ZOR-uz. Of course, in Portuguese it probably sounds more like MUSH.