The four sanctified months according to authentic Ahaadeeth are the months of Zul- Qa'dah, Zul-Hijjah, Muharram and Rajab. The sanctity of these months was observed in the Shariah of all the previous Prophets. "Allah Ta'ala made them (i.e. the four months) sacred and increased their sanctity. Hence He declared a sin therein more severe and increased the virtue of good deeds and the reward thereof." (Ibn Katheer Vol.2)
The best of fasts besides the month of Ramadhaan is the fast during Allah's month of Muharram and the best of Salaah besides the Faraaidh (obligatory salaah) is the Tahajjud Salaah (performed after midnight). (Muslim,Vol. 1)
THE DAY OF AASHURAH (10TH OF MUHARRAM)
The Tenth of Muharram, known as the day of Aashura, is a very significant day in the Islamic Calendar. Nabi (sallallahu alaiyhi wassallam) has exhorted the Ummah to fast on this day. Sayyadatina Aaisha (rahiyallahu anha) reports that Nabi (sallallahu alaiyhi wassallam) ordered the observance of the fast of Aashura.
Sayyadina Ibn Abbaas (radhiyallahu anhu) says: "I did not see Rasulullah (sallallahu alaiyhi wassallam) anxiously await the fast of any day, which he gave preference to (over other days), except this day of Aashura and the month of Ramadhaan." (Bukhari, Vol. 1)