Can anyone know when the Last Hour will come?

This knowledge is unique to Allah. No person, unless Allah wills, can know when it will take place. All we know is that it is coming, for it is revealed in the Qur'an:

People will ask you about the Last Hour. Say: "Only Allah has knowledge of it. What will make you understand? It may be that the Last Hour is very near." (Surat al-Ahzab, 63)

As revealed in the verse, nobody can have knowledge of the Last Hour unless Allah wills otherwise. However, one can make an estimate as to its century based on the hadith of the Prophet (saas) and signs in the Qur'an, and say "the Last Hour will come when there are no believers left and disbelief reigns." As a matter of fact, the great ahl al-Sunnah scholars al-Barzanji and as-Suyuti state, based on the hadith of the Prophet (saas), that the life span of the Ummah will not exceed the Islamic year 1500, in other words it will end before Islamic 1600s. Bediuzzaman Said Nursi says, again according to the information given in the hadith, that Muslims will remain on Allah's true path and will be victorious until around Islamic year 1506 with the Last Hour probably taking place in 1545 (2120 according to the Gregorian calendar). (Allah knows the truth) For detailed information on the subject, see http://www.awaitedmahdi.com/article.php?id=14883)