It is a requirement of the Holy Quran to show respect on the Meelad of Rasoolullah (sallal laahu alaihi wasallam). Allah Ta'ala says: "In the bounty of Allah Almighty and His Mercy, in that, let them rejoice, that is better than the wealth they accumulate". (Surah Yunus: 58) Almighty Allah had ordered us to rejoice on His Mercy and Rasoolullah (sallal laahu alaihi wasallam) is the greatest Mercy of Allah Ta'ala to all the Worlds.
In the time of Rasoolullah (sallal laahu alaihi wasallam), the period of the Sahabah and in the period of the Tabi'in, Meelad was not celebrated as it is done in the present form. But the Holy Prophet (sallal laahu alaihi wasallam), Sahabah or Tabi'in did not prohibit it as well. This is an accepted principle of Shari'ah that the performance of something is proof of Jawaaz (permissibility), and not doing it is NOT the proof of its prohibition.
The Meelad celebration is not compulsory. It is Mustahab (recommended). Imam Jalaaluddin Suyuti (radi Allahu anhu) said that it is Mustahab for us to celebrate Meelad of the Holy Prophet (sallal laahu alaihi wasallam) as to thank Allah. (Ruhul Bayaan)
Although the present form of Meelad is a Bid'ah (innovation) (Bid'ah Hasanah or Good Innovation), but the origin of Meelad is found in the time of Rasoolullah (sallal laahu alaihiwasallam). Rasoolullah (sallal laahu alaihi wasallam) himself made mention of his own Meelad by saying, "I am the Du'a of my father Hazrat Ebrahim (alaihis salaam), I am the good tidings of 'Isa (alaihis salaam), and I am the son of the two slaughtered ones (Hazrat Ismail - alaihis salaam and Hazrat Abdullah - radi Allahu anhu)."
The Holy Prophet's (sallal laahu alaihi wasallam) uncle and an arch enemy of Islam, Abu Lahab, set his slave Thuwaiba free being happy for the Meelad of Rasoolullah (sallal laahu alaihi wasallam). Abu Lahab's punishment is made light every Monday as a reward of his act, i.e. of expressing happiness for the birth of the Holy Prophet (sallal laahu alaihi wasallam). (Bukhari Shareef)
Rasoolullah (sallal laahu alaihi wasallam) expressed the virtues of Jummah (Friday) by saying that Hazrat Adam (alaihis salaam) was born on that day. Therefore, imagine the virtue of that day when Rasoolullah (sallal laahu alaihi wasallam) was born!
Hazrat Imam Shafi'i (radi Allahu anhu) said: "Any thing which opposes (or changes) the Quraan, Sunnah, Ijma (consensus) or the sayings of the Sahabah is Bid'ah. Any good deed which is not opposed to them is praiseworthy". (Meelad celebration does not oppose any of them)
Hazrat Moulana Abdus Sammi' (radi Allahu anhu) has counted 73 names of great scholars of Islam who wrote about the validity of Meelad celebrations. (Anwaare Saati'a)
Allama Jalaaluddin Suyuti (radi Allahu anhu) writes: "The Shari'ah commanded Aqeeqah on the birth (of a child). This is a way to thank Allah and rejoice, but on the time of death no such commandment has been given. In fact, mourning and grieving is prohibited. The same principle of Shari'ah demands that happiness and the joy should be expressed in Rabi-ul-Awwal on the birth of the beloved Rasool (sallal laahu alaihi wasallam) and not grieve on his Wisaal (Departure from this world)". (Husnul Maqsad Fee Amalil Moulid Al Haawi Lil Fatawa)
Imam Suyuti (radi Allahu anhu) writes about Meelad: "According to me, gatherings, recitations of the Quran, mentioning incidents of the holy life of Rasoolullah (sallal laahu alaihi wasallam) and mentioning those signs which appear at the time of his birth are amongst the good innovations in which a person is rewarded because in this there is respect, love and expression of happiness for the arrival of Rasoolullah (sallal laahu alaihi wasallam)". (Al Haavi Lil Fataawa)
Imam Qastalaani (radi Allahu anhu) writes: "In the month of the birth of Rasoolullah (sallal laahu alaihi wasallam) Muslims always had assemblies. In the nights of that month they gave charities and expressed happiness. They always increased good deeds in those nights. They always made arrangements to read the Meelad of Rasoolullah (sallal laahu alaihi wasallam) with the auspicious (hope) that Allah Ta'ala showers His blessings upon them. One of the experienced Barakah (blessing) of Meelad is that the year passes upon them peacefully. May Allah Ta'ala send His Blessings and Favour upon that person who took Meelaad-un-Nabi as Eid, so this Eid should become reason of hardness upon that person who has disease in his heart". (Mawahe bul Le Dunya)
Hazrat Sheikh Abdul Haqq Muhaddith Delwi (radi Allahu anhu) writes: "All Muslims have always celebrated Meelad functions in the month of Rabi-ul-Awwal. They always gave charities in the nights of that month and expressed their happiness. This is a common practice of Muslims that they particularly make mention of those incidents which are related to the birth of Rasoolullah (sallal laahu alaihi wasallam)". (Ma Sabata Bis Sunnah)