There are only two official holidays in Islam. One comes at the end of Ramadan and is called the 'Eid ul Fitr. (Festival of the Fast Breaking). The other comes at the end of the Hajj and is called the 'Eid ul Adha. (Festival of the Sacrifice.)
Some Muslims celebrate such things as the birthday of the Prophet, (Mawlud un Nabi), or the 'Eid ul Ghadir (which is a much later holiday centered on 'Ali, the Prophet's cousin, whom a group of Muslims called "Shi'a" revere), but standard Islam (Qur'an + Prophet's sayings and example) doesn't seem to give any overt or tacit support to these holidays. The Blessed Prophet said in authentic sayings that there were only two holidays in Islam, 'Eid ul Fitr and 'Eid ul Adha. The commemoration of the Prophet's birthday is debated among Muslim scholars.