^ Bro Aadil is talking about blessed days of the year, in most of them voluntary fasting is recommended (reward is bigger in these days). Like day of Arafah, and Day of Aashura'.
The following is not realted to Eid but could benefit inshaAllah :
Voluntary Fasting according to Sunnah:
1 - Six days of Shawwaal
Abu Ayyoob (may Allaah be pleased with him) reported that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever fasts Ramadaan and follows it with six days of Shawwaal, it will be as if he fasted for a lifetime.” (Narrated by Muslim, Abu Dawood, al-Tirmidhi, al-Nisaa’i and Ibn Maajah)
2 - First Nine days of Dhul-Hijjah (Especially 9th of Dul-Hijjah, Day of Arafah)
It was narrated from Ibn ‘Abbaas (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “There are no days on which righteous deeds are more beloved to Allaah than these ten days.” They said: “Not even jihad for the sake of Allaah?” He said: “Not even jihad for the sake of Allaah, unless a man goes out himself for jihad taking his wealth with him and does not come back with anything.” Narrated by al-Bukhaari, 2/457
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when the Messenger of Allah (sallallahu alaihi wa-sallam) was asked about the fasting on the day of Arafat, he said: “It expiates the sins of the previous year and that of the following year.” [Saheeh Muslim]
3 - Fasting The Day of Ashura
Ibn Abbas related : When the Prophet Muhammad (Blessings and peace of Allah be upon him) came to Madinah, he found (the Jews) fasting on the day of 'Ashura' (i.e. 10th of Muharram). They used to say: 'This is a great day on which Allah saved Moses and drowned the folk of Pharoah. Moses observed the fast on that day as a sign of gratitude to Allah. The Prophet Muhammad (Blessings and peace of Allah be upon him) said: "I am closer to Moses than them". So, he observed the fast (on this day) and ordered the Muslim to fast on it". [al-Bukhari and Muslim]
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Imam Muslim narrated from Ibn Abbas, he said: "When the Messenger of Allah (Blessings and peace of Allah be upon him) fasted on the day of Ashura and commanded that it should be observed as a fast, they (his Companions) said to him: Messenger of Allah, it is a day which the Jews and Christians hold in high esteem. Thereupon, the Messenger of Allah (peace be upon him) said: When the next year comes, God willing, we would observe fast on the 9th . But the Messenger of Allah (Blessings and peace of Allah be upon him) died before the advent of the next year".
4 - Fasting Mondays and Thursdays
Abu Hurairah reported that the most the Prophet would fast would be Monday and Thursday. He was asked about that and he said: "The actions are presented on every Monday and Thursday. Allah forgives every Muslim or every believer, except for those who are boycotting each other. He says [about them]: 'Leave them.' " This is related by Ahmad with a sahih chain. It is recorded in Sahih Muslim that the Prophet, when asked about fasting on Monday, said: "That is the day on which I was born and the day on which I received revelations."
5 - Fasting most of the month of Sha'ban (the month preceding Ramadan)
The Prophet would fast most of the month of Sha'ban. 'Aishah said: "I never saw the Messenger of Allah fast a complete month save for Ramadan, and I have never seen him fast more in a month than he did in Sha'ban." This is related by al-Bukhari and Muslim.
6 - Fasting three days of every month
Abu Zharr al-Ghafari reported: "The Messenger of Allah ordered us to fast for three days of every month--that is, on the days of the full moon (the 13th, 14th, and 15th of the lunar month). And he said: 'It is like fasting the whole year.' " This is related by an-Nasa'i and by Ibn Hibban, who called it sahih.
7 - Fasting one day and not fasting the next
Abu Salama ibn 'Abdurrahman reported from 'Abdullah ibn 'Amr that the Prophet, upon whom be peace, said to him: 'I have been informed that you stay up in prayer during the night and fast during the day. 'Abdullah answered: "Yes, O Messenger of Allah." The Prophet said: "Fast and do not fast, pray and sleep, for your body, your wife, and your guests have a right upon you. It is sufficient for you to fast three days a month." 'Abdullah said: "I wanted to be stricter on myself and I said: "O Messenger of Allah, I have the strength to do more." The Prophet said: "Then fast three days a week." 'Abdullah said: "I have the strength to do more!" The Prophet said: "Fast the fast of the Prophet David and do not do more than that!" 'Abdullah inquired: "And what was the fast of David?" The Prophet replied: "He would fast one day and then not fast the next." This is recorded by Ahmad and others.
