None of these religions purports that it is exclusively "their holy city", i.e. its mine and no-one else's, although the Islamic Waqf of Al-Aqsa Mosque and the Haram Al-Sharif routinely tries to discredit the Jewish connection of the city in order to buttress Palestinian claims. (The Waqf somehow avoids the problem of Christianity holding the city as holy, though.)
Jews acknowledge Christian and Muslim reverence of the city and this is most clearly noted by the permission given by Israel for Muslims and Christians to visit and regulate their holy places in the Old City.
Christians acknowledge the Jewish history of Jerusalem since it undergirds Jesus' activities in the Holy Land. Christians do not actively recognize the Muslim holiness of the place, but have not attempted to refute it either.
Proper Muslims acknowledge both the Jewish and Christian reverence of the city since King David, King Solomon, and Jesus are all Islamic Prophets.
To find out what particular parts of Jerusalem each finds holy, please see the Related Question.
Jews, Muslims, and Christians
Jerusalem is considered holy by Muslims, Jews, and Christians.
jerusalem?
Jews, Muslims, and Christians :)
Jerusalem is the Holy City for Christians, Jews, and Muslims.
Jerusalem.
Jerusalem
Muslims believe that Jews and Christians corrupted the Scriptures given to them with the purpose of strengthening their power.
Since the Muslims believe that Jews and Christians were "People of the book", they received special treatment.
For Judaism: http://judaism.answers.com/jewish-history/jerusalem-in-judaism
Christians, Jews, and Muslims
Jerusalem is considered Holy by Jews, Christians, & Muslims alike. For Jews, it is where their temples were built; for Christians it was where Christ Rose from the Dead; for Muslims, it is where Muhammad a dream where he ascended to Heaven.