As a Hebrew name, it is usually pronouced similar to its roots in Shalom, but I've heard in English and French as Sa-Lo-May. I prefer the former.
-- Anonymous User 8/13/2007
According to American Heritage Dictionaries, Salome is pronounced sah-LO-mee and SA-lo-may. I prefer the latter, as sa-LO-mee is too similar to salami.
I've read about four or five different possible pronunciations of Salome in these comments here and everyone seems very sure that his/her given pronunciation is the right one. So I suppose it's not a name that a child would have fun with if you lived in an English-speaking country. I always thought, it would be pronounced SA-lo-may in English, but apparently, it's not that easy.
In Germany (and I claim to be certain here, as I am German), it is pronounced like ZAH-loh-meh, but not exactly as it's difficult to describe the pronunciation well.
It *IS* Suh-LO-mee in English. Which is closer to the Hebrew original SHLOMIT or SHLOMITZION. The French, Spanish and Italian pronunciations tend to sound more like Sah-lo-MAY (which incidentally sounds horrific when pronounced by native English speakers).