Islam is something of a peculiar religion when it comes to festivals in two ways. One, it doesn't have a whole lot of them—at least, not a lot that anyone pays attention to. Two, they are linked to the Islamic calendar, which is purely lunar: it is only 354 days long, or about 11 days shorter than the solar year. These two peculiarities are related: because of the length of the Islamic year, the months move through the seasons. Since so many festivals are linked to seasons and seasonal events (like planting or the harvest or the solstice), it would be very difficult to link them to the Islamic calendar. As a result, while seasonal festivals exist in many if not most Muslim countries, they tend to be culturally-based and linked to local solar or lunisolar calendars, many of which date from pre-Islamic times. For instance, the Egyptian spring festival, Sham el-Nessim, is linked to the Egyptian calendar, which is more or less the same as the old Roman Julian calendar (it falls on Orthodox Easter Monday for historical reasons). By the same token, the Iranian spring festival, Nourouz, falls on the first day of the Iranian solar calendar, which is based on the Islamic calendar and the pre-Islamic Persian and Hindu ones. As a result, Islamic holidays are fairly few and far between. However, there are several ones worth mentioning. For reference, the Muslim months are:
The New Year (1 Muharram)A fairly unimportant holiday, which often goes completely unnoticed today. There are only two interesting things about it.
Ashura (10 Muharram)A pretty much strictly Shiite holiday, commemorating the defeat of The Prophet Muhammad's grandson Husayn in the Battle of Karbala (in Iraq) in the Hijri year 61 (680 CE). Since Shiites regard Husayn as having a right to be the Caliph, they understandably regard the day as one of mourning; salty foods (representing salty tears) are eaten, and self-flagellation and other forms of self-injury (including, famously, cutting the forehead with a sword) are common forms of remembrance. Also, prayer. Lots of prayer. Sunnis tend to ignore the holiday, although some believe that the aforementioned tradition of fasting on 1 and 2 Muharram actually applies to the 9th and 10th or 10th and 11th of Muharram; since the custom is based on a report of something the Prophet did, it's not unexpected that there are conflicting reports. This corresponds more closely to the date of Yom Kippur (10 Tishrei); Muslim months always start on the same day or almost the same day as Jewish months, as the Jewish calendar is lunisolar. There is also a cultural custom in Egypt and Turkey to eat a certain kind of pudding with nuts and dried fruit, also called Ashura, on that day; what it has to do with anything is unclear. Bizarrely, the festival has also spread to the English-speaking Caribbean, particularly Trinidad and Tobago and Jamaica, where it is known as Hosay (after Husain). It was brought by Shia indentured labourers from British India, and was adopted by Hindu Indian labourers as well, as a gesture of cultural solidarity. Eventually, the practice became much more widespread; it is celebrated with the construction of impromptu mosques out of paper and tinsel, along with a lot of balloons. The practice is by no means universal, but it has seen a revival in recent years.
Arbaeen (20 Safar)A strictly Shia holiday, commemorating the fortieth day after Ashura (the name means "forty" in Arabic; it is also known as Chehelom, which is the same thing but in Persian). A common date for Shias to go on pilgrimage to Karbala.
Mawlid an-Nabi (Birthday of the Prophet) (12 or 17 Rabi` al-Awwal)A holiday whose importance varies from place to place. In some countries, it's a big deal, a full day off with parades and special prayers and so on; in some other ones, like Saudi Arabia, it is banned. There is a long and complicated theological debate about this, with ulema (religious scholars) having some pretty heated arguments about whether it is allowed or not. (There really should be a Muslim version of Jews Love to Argue.) There is also a difference over the date; Sunnis and some small Shia sects recognize 12 Rabi` al-Awwal, while most Shia recognize 17 Rabi` al-Awwal.
Isra' and Mi`raj (27 Rajab)Commemorates the night when Muhammad, according to Muslim tradition, was transported to Jerusalem on a winged horse, met and prayed with all of the prophets, and then was lifted up to heaven to have a personal chat with God, receiving some commandments in the process. Although pretty much all Muslims know the story, very few commemorate it at all, and many aren't even aware the holiday exists. Those who do know about and observe the holiday tend to restrict their celebration to an extra prayer at night, although in some places they string lights up around town and tell the story to young children, attracting them to the mosque with candy.
Nisf Sha`ban (15 Sha`ban)Literally "halfway through Sha`ban", this has no particular religious significance, but it is widely seen as good time to start warming up for Ramadan. Observant Muslims tend to go on a voluntary fast on this day, and stay up late or even all through the night, praying. These are both activities associated with Ramadan, so it makes a fair amount of sense. Some continue to do this for the rest of Sha`ban, while some might only fast a few more days between the 15th and the first day of Ramadan.
RamadanNot so much a holiday or a festival as a duty. Able-bodied, adult, non-poor Muslims must fast from dawn to sunset. Fasting in Islam means no eating, no drinking (not even water!), no smoking, no sex, and avoiding swearing and evil thoughts if you can help it. The idea is encouraging holiness and solidarity with the poor (Muhammad had lived as a poor orphan, and social justice is a big part of Muslim belief). Muslims are also supposed to pray long into the night, in a special form of prayer called Tarawih. The idea behind this is that the whole Qur'an should be read over the course of the month; to make this easier, the Qur'an has been divided in to 30 parts of roughly equal length, which, given that the Qur'an is actually quite short compared to most religious texts, makes the task fairly manageable. That said, Muslims do make things festive during Ramadan. People tend to put up lights rather like Christians at Christmas, and children dance around with lamps. The two meals of the day—Suhur, before the fast, and Iftar, at sundown breaking the fast—tend to be heartier and tastier than their normal-time equivalents (although the latter factor could be because people are usually famished after fasting all day), and are often family affairs. Friday Iftar tends to be a big feast with extended family; in places where extended families aren't available (e.g. in the West), Muslims tend to get together with the congregation instead. In some places, mosques and rich people put out big tables full of food for the poor during Ramadan; sometimes, the food can be quite rich.note The intersection of Ramadan and modernity has also created a fair amount of Fantastic Religious Weirdness. The most obvious thing is that there are now Muslims living all over the world, which has an effect on the dawn-to-sunset requirement: Muslims living in high-latitude countries like Britain and Norway experience ridiculously short days in the winter and ridiculously long ones in the summer, making the winter fast almost absurdly easy and the summer fast torturously difficult in these places. Various authorities have spoken to the issue, variously advising these Muslims to fast for twelve hours (six o'clock in the morning to six o'clock in the evening is typical, but seven to seven or eight to eight would also be reasonable) during the day no matter when Ramadan falls, to fast with Mecca (which is low-latitude and never fasts more than 13 hours or less than 11 hours), or to select another lower-latitude location and fast with them. Still others have advised their followers to suck it up. Other weirdness comes from technology. Wealthy Gulf Arabs, among others, have been known to jet off to high-latitude places experiencing winter that Ramadan for the month to shorten the fast. Since right now Ramadan falls in Northern Hemisphere summer, these guys tend to go to Chile, Argentina, New Zealand, and southern Australia; in about fifteen years, Alaska, Canada, Iceland, Scotland, Scandinavia, and Russia should be more popular. Clerics have condemned the practice of going somewhere just to fast less in no uncertain terms; those with the means to do so have started, very conveniently, to happen to have long business trips and long-scheduled vacations in those countries. Still other weirdness comes from the nature of modern work. Since fasting can seriously drain your ability to do anything, many Muslim countries provide for shortened work hours during Ramadan. Some businesses just close during the day and operate at night. As a result, many Muslims spend their fasting days languishing about the house, watching television, particularly soap operas. Indeed, many soaps in the Middle East are made specifically for Ramadan—since Arab, Turkish, and Iranian soaps tend to be of the Latin American School, this works quite well.
Laylat ul-Qadr (The Night of Power) (Odd-numbered day in the last week or so of Ramadan, very often the 27th)This is a very religious holiday, with multiple significance. It marks the beginning of the revelation of the Qur'an to Muhammad, and is also supposedly the day on which the fate of everything in the world is sealed for the year (rather like the Jewish belief about Yom Kippur). It is generally accepted practice to pray all night that day; even men who don't show up for Tarawih often go to the mosque on this night. Some very devout people move into the mosque for the last ten days of Ramadan, spending all their time praying and reading the Qur'an, except when they have to sleep or eat.
Eid al-Fitr (1 Shawwal)The Feast of the Breaking of the Fast, marking the end of Ramadan. One of Islam's biggest festivals, marked with a wide array of festivities and rituals. As is typical for a Muslim holiday, it is associated with certain religious observances; chief among them are Zakat ul-Fitr and Salat al-Fitr. The former is a donation to charity, required for anyone who can afford it, for the support of the poor. The latter is a large group prayer—in many places, people have to pray in the street because the mosque is too crowded—with certain extra rituals and (often) an extra-long sermon. These are usually carried out in the early-to-mid-morning, well after sunrise: you have to give people time to eat while the sun is up (remember, something they haven't been able to do in a whole month). Everybody typically wears their best clothes. The rest of the day is typically devoted to all kinds of fun: inevitably, there's a truly massive family feast in which everyone pulls out all the stops, typically sometime in the afternoon. Snacking, particularly on sweet foods, is common all through the day. Children are traditionally given gifts and/or money. And no matter where you go in the Muslim world, every culture has its own unique sort of public festivity.
Eid al-Adha (10-13 Dhul Hijjah)The Feast of the Sacrifice. The biggest festival of the Muslim year, as indicated by its length (four whole days, although most folks only get the first day off). It commemorates the Sacrifice of Abraham, in which Abraham, on God's command, took his son Isma`il up a hill, trussed him up like a sacrificial lamb, and brought out his knife, when God miraculously whipped Isma`il away and replaced him with a lamb. Sound familiar? The Bible has the same story, except that it's Isaac (Ishaq in Islam) rather than Ishmael (Isma`il in Islam) who is the subject. Significantly, Ishmael is legendarily one of the ancestors of the Arabs, and of Muhammad's Quraish tribe in particular, while Isaac was of course the patriarch of the Hebrews. So there's that. Anyway, the feast marks the end of the Hajj (the annual pilgrimage to Mecca), and is celebrated similarly to Eid al-Fitr. There are three main differences between the way this holiday and Eid al-Fitr are celebrated, namely: