How has the relationship between Islam and other faiths changed through the centuries, and why has this change occurred?

First, we should note that Islam is not monolithic. There are various branches of Islam, and various individual imams or religious leaders and scholars who set forth different opinions about matters of faith and interpretation of the Koran, leading to varying attitudes about other faiths.
The Koran itself distinguishes between the "peoples of the book," or the Abrahamic religions, and other religious faiths, which are considered forms of idolatry. Islam shares a common core of faith with Judaism and Christianity, accepting that the sacred texts and prophets of the other Abrahamic religions represent genuine revelations of Allah, although incomplete, while Mohammed provides a later and more comprehensive revelation; in certain ways, Islam regards Christianity and Judaism the way Christianity sees Judaism. The Zoroastrians were often grouped among the peoples of the book.
In the medieval period, Jews, Christians, and people of certain other faiths were allowed a considerable degree of freedom within Islamic territories, including freedom of worship. In the sixth through twelfth centuries, Baghdad was a refuge for Platonists, Jews, and Christian "heretics" fleeing persecution. As Islam became more legalistic after the twelfth century, in many areas this degree of openness diminished or disappeared.
In more recent times, the Ahmadiyya branch of Islam emphasizes its continuity with other religions of the book, and the Alawites are syncretistic, adopting some Christian traditions. Sufis and Malaysian Muslims are traditionally more open to other religions and accepting of religious diversity than Sunni Salafists.