The word "meme" was borrowed from Richard Dawkins' concept of "a unit of cultural transmission" in his 1976 book, The Selfish Gene. In that book, he specified that it should rhyme with "cream," and presumably since we've hijacked the term from him we would adopt his pronunciation as well. :)
A quote from the book:
"We need a name for the new replicator, a noun that conveys the idea of a unit of cultural transmission, or a unit of imitation. ‘Mimeme’ comes from a suitable Greek root, but I want a monosyllable that sounds a bit like ‘gene’. I hope my classicist friends will forgive me if I abbreviate mimeme to meme. If it is any consolation, it could alternatively be thought of as being related to ‘memory’, or to the French word même. It should be pronounced to rhyme with ‘cream’."