A book I just finished had a discussion of the early history of Islam. According to this author, Mohammed believed that he had received a revelation for the Arab peoples, who at that time were predominantly pagan. There were a few Christians and Jews in Arabia at the time, so Mohammed was familiar with them, although his knowledge of the Hebrew scriptures was pretty vague until he went to Medina and had a chance to study with the Jewish community there. The author made a distinction between the initial teachings of Islam about the status of other religions, and what developed over the course of a few hundred years of Arab imperialism. It seems that under Mohammed and the first four caliphs, Islam explicitly acknowledged the validity of the Jewish and Christian revelations, and did not force people of those faiths to convert. Only later did Islam begin to assert that theirs was the only "right" religion.
Muslims who are peaceful tend to hearken back to this early period of acceptance of other monotheistic religions. Islamic fundamentalism is actually a fairly recent phenomenon, historically speaking. It emerged most strongly under the Wahhabist sect 200 years ago. Historically, Islam has been much more diverse in its belief than is ordinarily portrayed in the western media. The literal interpretation of the Koran was only one of many strands of Islam. In past times, for example, various forms of Sufism, a mystical form of Islam which interprets the Koran in a much more nuanced sense, were followed by a majority of muslims.
The present state of Islam, and the predominance of fundamentalism, can probably be traced to the rise of the West and the eclipse of Islam as a world power. Rather than rising to the challenge posed by Europe, and striving for a comparable development of its own, the Islamic world retreated. Western culture values innovation, creativity and change, and these cultural values have driven the advancement of science and technology. And you can't simply mimic or copy creativity. As a whole, the Islamic world seems to have a cultural inferiority complex. Combine this with memories of former cultural greatness, lack of democratic institutions, and little separation between church and state, and you have the formula for the sort of fundamentalism that emerged.
So, in specific answer to your question: there are far too many muslims willing to engage in violence, and so today I would say that Islam on balance is not a peaceful religion. Of course Judaism and Christianity have periods of violence in their histories, too. Hopefully Islam will also come to understand that "Thou shalt not murder" means that God does not want us to kill others in His name.
Let me be the first.