Returning the greeting according to Quran and Sunnah :
When you are greeted with a greeting, greet in return with what is better than it, or (at least) return it equally. Certainly, Allâh is Ever a Careful Account Taker of all things. [The Noble Qur'an An-Nisa 4:86]
Ibn Katheer raheemahullaah explained this verse by saying: "If the person greeted you with the Salaam (Assalamu alaykum) you should reply in a better form, or reply similarly. However, the extended form is preferable, but the shorter is compulsory. Which means that greeting is preferable but the greeting in return is compulsory, and it should be in the form of the Salaam (assalamu alaykum) and not in any other form."
The Prophet said, "Allah created Adam, making him 60 cubits tall. When He created him, He said to him, "Go and greet that group of angels, and listen to their reply, for it will be your greeting (salutation) and the greeting (salutation) of your offspring." So, Adam said (to the angels), As-Salamu Alaikum (i.e. Peace be upon you). The angels said, "As-salamu Alaika wa Rahmatu-l-lahi" (i.e. Peace and Allah's Mercy be upon you). Thus the angels added to Adam's salutation the expression, 'Wa Rahmatu-l-lahi.' Any person who will enter Paradise will resemble Adam (in appearance and figure). People have been decreasing in stature since Adam's creation.
[Hadith - Sahih Bukhari 4.543, Narrated Abu Huraira, radiya Allah 'anh]
When those who believe in Our Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.) come to you, say: "Salâmun 'Alaikum" (peace be on you); your Lord has written Mercy for Himself, so that, if any of you does evil in ignorance, and thereafter repents and does righteous good deeds (by obeying Allâh), then surely, He is Oft*Forgiving, Most Merciful.
[The Noble Qur'an Al-An'am 6:54]
The Messenger of Allah, observed: You shall not enter paradise so long as you do not affirm belief (in all those things which are the articles of faith) and you will not believe as long as you do not love one another. Should I not direct you to a thing which, if you do, will foster love amongst you: (i.e.) give currency to (the practice of paying salutation to one another by saying) as-salamu alaykum.
[Hadith - Sahih Muslim 96, Narrated Abu Hurayrah]
Read also:
The importance of saying "Assalaamu 'alaykum" and returning the greeting
http://www.turntoislam.com/forum/showthread.php?p=3827
"Assalaamu 'alaykum" = The Muslim greeting
The Prophet (peace and blessings of Allaah be upon him) also explained the reward earned by the one who says salaam, as was reported by al-Nisaa’i in ‘Aml al-yawm wa’l-laylah (368) and al-Bukhaari in al-Adab al-Mufrad (586) and by Ibn Hibban (493). They reported from Abu Hurayrah (may Allaah be pleased with him) that a man passed by the Messenger of Allaah (peace and blessings of Allaah be upon him) whilst he was sitting with some others, and said “Salaam ‘alaykum (peace be upon you).” The Prophet (peace and blessings of Allaah be upon him) said, “[He will have] ten hasanaat (rewards).” Another man passed by and said “Salaam ‘alaykum wa rahmat-Allaah (peace be upon you and the mercy of Allaah).” The Prophet (peace and blessings of Allaah be upon him) said, “[He will have] twenty hasanaat.” Another man passed by and said “Salaam ‘alaykum wa rahmat-Allaahi wa barakaatuhu (peace be upon you and the mercy of Allaah and His blessings).” The Prophet (peace and blessings of Allaah be upon him) said, “[He will have] thirty hasanaat.”