I'll leave the exact details of the Muslim beliefs about end times to someone more theologically inclined. However, yes, off the top of my head I can think of two very significant events inspired Millenarian beliefs: the Safavid takeover of Iran and the 1979 takeover the Haram al-Sharif in Mecca.

I talk about the Safavid takeover of Iran (this is how Iran became Shi'a) in this older comment (particularly in the follow up comment). Shah Ismail, the first of the Safavids to rule to Azerbaijan and Iran, declared himself Mahdi (the forerunner to Mesih, the Messiah, and generally the important figure in Muslim eschatology) in the early 16th century. He came from a religious and noble heritage (his predecessors were heads of the Safaviyya Sufi order, and he was descended from both the Prophet Muhammed and Byzantine Emperors). For most of his life before his rise to power, after his other relatives were killed, he was raised in isolation by other clerics. The Safavid takeover in Iran is one of the most unexpected and fascinating moments in history, up there with the surprise and speed of the initial Arab conquests in the 7th century. Obviously, the end of the world did not happen in his life, and his successor set up a stable dynasty that lasted over two centuries. But his initial success was a military coalition of mainly Turkic tribes who clearly believed that he, Ismail Shah, was the promised Mahdi. Since the period of Ismail Shah's rule, and particularly the Ottoman reaction to it, set up the Sunni-Shi'a split that continues to the present day, I think this unambiguously qualifies for a "notable event". From his emergence until his defeat at the Battle of Chaldiran (1514), there was relatively little strife in his messianic followers. That battle opened the door for strife because, since it was a defeat, it suggested that Shah Ismail wasn't divinely invincible. It suggested this not only to his followers, but to the Shah himself, and he played a much smaller role in the decade between Chaldiran and his death than he did in the decade and a half leading up to the battle. I don't know how reliable the sources are (i.e. whether they written by his or his son's political enemies) but some report that he fell to the drink after this turning point. After his death, with no messianic figure leading them, the Safavid lands collapsed into a ten year civil war (civil wars were actually quite common consequences of succession disputes in the region at the time, though ten years is certainly on the longer end). Still, the Safavid dynasty was able to consolidate power and Shi'a Islam did become an important rival to Sunni Islam from the sixteenth century onward.

The other major event that immediately comes to mind is the 1979 Seizure of the Haram al-Sharif in Mecca (the Haram al-Sarif, also called the Noble Sanctuary or the Grand Mosque, is the home of the Kabaa and so the direction that all Muslims pray). During the Hajj that year, Mohammed Abdullah al-Qahtani was declared to be the Mahdi by a group of four to five hundred fervent believers led by his brother-in-law. It was a truly shocking event, and the armed group holed up in the Mosque sanctuary for about two full weeks, at points broadcasting their message from the mosque speakers. It's worth noting that, by the Islamic calendar, this occurred at the very start of the year 1400 and followers drew explicit comparisons between Mohammed Abdullah al-Qahtani and his father and the Prophet Mohammed and his father. Though eventually put down with Pakistani and finally French help (it's widely alleged that several French special forces commandos underwent a pro-forma conversion to Islam in order to enter the holy city of Mecca and end the uprising). All told, several hundred people (including militants, civilians, and Saudi military and police forces) were killed. This was a big turning point for the Saudi state, and marked perhaps the first point that their close relationship with the ulema--the clerical bureaucracy--was seen as a liability rather than just an asset. Many of the participants were themselves members of the ulema--this was not just a group of uneducated peasants or nomads. Further, this was the first time that the Saudi State took militants seriously in general, and most Saudi "anti-terrorism" measures and military cooperation with the West can be traced to this event (which happened shortly after the Islamic Revolution in Iran, which also made many leaders in the region quite wary of the clerics in their countries). However, it should be made very clear that the Saudi State reacted not by limiting religion, but by closely watching it and empowering it--particularly those of a particular style that received even more state sponsorship than before. Gender segregation was extended. Women were slowly pushed out of newspapers and off television, and Western imports like cinema were restricted and then closed. This increased religiosity gave the Saudi State more control over people, and it allowed them to make sure that they were getting a very clear, rigorous, and state-selected religious agenda (this eventually led to the marginalization of other, more moderate groups in the Kingdom, including the Muslim Brotherhood, who had been gaining influence in the Gulf at least through the 1950's and 60's). Here, the event wasn't so much notable as the reaction.

Edit: Oh, man, I forgot my favorite Mahdi claimant! I won't get into him, Muhammad Ahmad of Sudan, whose partially messianic, partially anti-colonial wars are most commonly called the Mahdist War.

The two other important Mahdi claimants of the 19th century can in someways be compared to Joseph Smith who founded Mormonism. Mirza Ghulam Ahmad's movement is today known as Ahmaddiyya. Ali Muḥammad Shirazi, known as the Bab, claimed to be the Mahdi and founded the movement known as Babism. As Mahdi, he foretold the coming of one greater than he (perhaps comparable to the role John the Baptist plays in Christianity). After the Bab's death, most of his followers agreed that this next promised was Mirza Husayn-Ali Nuri, better known as the Bahá'u'lláh, who founded the Baha'i Faith and claimed to be not just the fulfillment of the Bab's prophecy, but all Christian, Muslim, Jewish, Hindu, Buddhist, and other groups' eschatological prophecies. Neither of their claims were particularly apocalyptic, to my knowledge, and both concentrated heavily on building movements rather than the immanent end of the world. Since participation in either movement is widely seen as making one an apostates in the Muslim World (similar to how Mormonism was long seen in the Christian World), Baha'is and Ahmadis are among the most persecuted religious groups in the world today. There are probably 10-20 million Ahmadis (mostly in South Asia and some Muslim-majority parts of Africa), and probably about six million Baha'is (spread surprisingly evenly all over the world, with the largest population still probably in Iran, but hugely prosecuted since the Islamic Revolution).