There is a greeting I have often heard among Muslims. (Thanks to Geeo in the comments for helping me find the "correct" spelling of the phrase, which made searching for it easier):
To which there is a "traditional" reply as well:
Wa alaykumu s-salam
What do these phrases mean? Do they carry religious meaning or connotations, or are they used by non-Muslim Arabic-speakers as well? Would it be offensive (or at least out of place) if, as a Caucasian non-Muslim middle-class young male, I greeted a Muslim or Arabic speaker with this expression?