Sheikh M. S. Al-Munajjid, a prominent Muslim Scholar states:
Fasting on the two days of `Eid is haram (forbidden), as indicated by the hadith of Abu Sa`id Al-Khudri (may Allah be pleased with him) who said: The Prophet (peace and blessings be upon him) forbade fasting on the day of Al-Fitr and [the day of] An-Nahr [Sacrifice]” (Al-Bukhari and Muslim). The scholars are unanimously agreed that fasting on these two days is haram.
It is also haram to fast on the Days of Tashreeq, which are the three days after `Eid Al-Adha (11, 12 and 13 Dhul-Hijjah) because the Prophet (peace and blessings be upon him) said: “The Days of Tashreeq are days of eating, drinking, and remembering Allah” (Muslim).
Click Here to find out which other days are forbidden to fast.