This excerpt is taken from Sheikh Abu Hamza Abdul Khaliq Siddiqi's book Sahih Fazail-e-Amaal.
Allah Almighty has said:
﴿وَإِذَا حُيِّيتُم بِتَحِيَّةٍ فَحَيُّوا بِأَحْسَنَ مِنْهَا أَوْ رُدُّوهَا ۗ إِنَّ اللَّهَ كَانَ عَلَىٰ كُلِّ شَيْءٍ حَسِيبًا﴾
"And when you are greeted with a greeting, greet in return with what is better than it, or (at least) return it equally. Indeed, Allah is ever, over all things, an Accountant."
Reference: (4-An-Nisa:86)
Hafiz Ibn Kathir, may Allah have mercy on him, writes: "All the scholars of Islam agree that giving salam is Sunnah, and responding to it is obligatory. These scholars have used this very verse as evidence, and the reason is also that not responding to salam is a disrespect to a Muslim, which is forbidden. Hasan al-Basri and Sufyan al-Thawri and others hold the same view."
عن عبد الله بن عمرو بن العاص رضي الله عنهما أن رجلا سأل النبى صلى الله عليه وسلم أى الإسلام خير؟ قال: تطعم الطعام، وتقرأ السلام على من عرفت ومن لم تعرف .
It is narrated from Sayyiduna Abdullah bin Umar and bin Aas, may Allah be pleased with them, that a man asked the Messenger of Allah, peace and blessings be upon him: Which deed in Islam is the best? The Prophet, peace and blessings be upon him, said: "Feed the hungry, and greet every person with salam, whether you know them or not."
Reference: Sahih Bukhari, Book of Faith, Chapter: Feeding Food from Islam, Hadith: 12.
عن أبى هريرة رضى الله عنه قال: قال رسول الله صلى الله عليه وسلم : لا تدخلون الجنة حتى تؤمنوا، ولا تؤمنوا حتى تحابوا، أولا أدلكم على شيء إذا فعلتموه تحاببتم؟ أفشوا السلام .
It is narrated from Sayyiduna Abu Hurairah, may Allah be pleased with him, that the Messenger of Allah, peace and blessings be upon him, said: "You will not enter Paradise until you believe, and you will not believe until you love one another. Shall I tell you something that if you do it, you will love one another? Spread salam among yourselves."
Reference: Sahih Muslim, Book of Faith, Chapter: Clarifying that only the believers enter Paradise, and that loving the believers is part of faith, Hadith: 45.
عن عمران بن الحصين رضي الله عنهما قال: جاء رجل إلى النبى صلى الله عليه وسلم فقال: السلام عليكم، فرد عليه السلام، ثم جلس، فقال النبى صلى الله عليه وسلم : عشر . ثم جاء آخر فقال: السلام عليكم ورحمة الله، فرد عليه فجلس، فقال: عشرون . ثم جاء آخر، فقال: السلام عليكم ورحمة الله وبركاته، فرد عليه السلام فجلس، فقال: ثلاثون .
It is narrated from Sayyiduna Imran bin Husain, may Allah be pleased with him, that a man came to the Prophet, peace and blessings be upon him, and said: As-salamu alaykum! The Prophet, peace and blessings be upon him, replied to his salam. Then the man sat down. The Prophet, peace and blessings be upon him, said: "(He will have) ten (good deeds)." Then another man came and said: As-salamu alaykum wa rahmatullah, the Prophet, peace and blessings be upon him, replied to his salam, then he sat down. The Prophet, peace and blessings be upon him, said: "Twenty (good deeds)." Then a third man came and said: As-salamu alaykum wa rahmatullah wa barakatuh, the Prophet, peace and blessings be upon him, replied to his salam, then he sat down. The Prophet, peace and blessings be upon him, said: "Thirty (good deeds)."
Reference: Sunan Abi Dawood, Book of Manners, Chapter: How is Salam? Hadith: 5195. Sunan Tirmidhi, Chapters of Seeking Permission, Chapter: What is mentioned about the virtue of Salam, Hadith: 2689.
Al-Albani, may Allah have mercy on him, declared it "Sahih."