{hur-my'-uh-nee}

I don't read a ton of Greek literature, but occassionally I do and I have to admit that the names throw me for a loop sometimes. I found a lovely site -- Encyclopedia Mythica -- which is not only a great source for the mythic stories, but has a handy pronunciation guide. It covers most of the Greek and Roman myths, some Celtic names, and some Native American stories, as well. Not comprehensive, but a good reference for the most common stuff.

I have to admit that even though I knew that Hermione was pronounced {hur-my'-uh-nee}, every time I read it in Harry Potter, I heard her-mee-ohne in my head. And, if you pick up the new YA series 'Percy Jackson and the Olympians' by Rick Riordan (The Lightning Thief and The Sea of Monsters) it's handy to know how to pronounce the Greek names