Abu Hurairah (May Allah be pleased with him) reported: The Prophet (PBUH) said, "When Allah created Adam (PBUH), He said to him: `Go and greet that company of angels who are sitting there - and then listen to what they are going to say in reply to your greetings because that will be your greeting and your off-spring's.' Adam (PBUH) said to the angels: `As-Salamu `Alaikum (may you be safe from evil).' They replied: `As-Salamu `Alaikum wa Rahmatullah (may you be safe from evil, and Mercy of Allah be upon you).' Thus adding in reply to him: `wa Rahmatullah (and Mercy of Allah)' to his greeting.''
[Al-Bukhari and Muslim].

Commentary: The Islamic form of greeting - As-Salamu `Alaikum (may you be safe from evil) - has been in existence since the days of Prophet Adam. According to some Ahadith, it is better to add in response: wa Rahmatullahi wa Barakatuhu (and the Mercy and Blessings of Allah).