Praise be to Allah.
As Muslims, we celebrate only two eid (festivals): eid ul-fitr (after the end of Ramadhan), and eid ul-Udh-ha, the day of the greater hajj (pilgrimage). During these two festivals, we offer felicitations, spread joy, and entertain children. But more importantly, we offer remembrance of Allaah's blessings, celebrate His name and offer the eid salaat (prayer). Other than these two occasions, we do not recognize or celebrate any other days in the year.
Of course, there are other joyous occasions for which the Islamic shariah dictates appropriate celebration, such as gathering for special meals during weddings or on the occasion of the birth of a child (aqeeqah). However, these days are not specified as particular days in the year; rather, they are celebrated as they happen in the course of a Muslims life.