A standard greeting, with some Islamic connotation is:

Peace be upon you - أسَّلامُ عَليكُم (ah’salaamu ah’leeokum) with the response و عَليكُم السلام (wa ah’leeokum a’salaam) - And peace be upon you (reply)

Sometimes you may hear added on, أسَّلامُ عَليكُم و رحمة الله (ah’salaamu ah’leeokum wa rahmatu allah), which means “Peace be upon you and Mercy of Allah”.

Or, you might hear an even longer greeting: أسَّلامُ عَليكُم و رحمة الله و بركات (ah’salaamu ah’leeokum wa rahmatu allah wa barakatuh) - “May the Peace, Mercy and Blessings of Allah be upon you”

This article in the Arab News explains more about the use of greetings in Arabic:

Muslims all over the world use the Islamic form of greeting, assalamu alaikum, which means “peace be to you.” The very wording helps generate a friendly and relaxed atmosphere. It is also common in its shorter and longer forms to all Muslim communities wherever they happen to be. Thus, when two Muslims meet who are total strangers to each other, the moment they use this greeting, they immediately feel that they have common ground, even though they do not speak each other’s language. The Islamic greeting has different versions, the shortest of which is the one we have already mentioned. The rule in Islam is that when we are offered a greeting, we return it with a better one, or with its equal at least. (read more)