The very first universities had a religious basis, with the first three universities ever founded and still in existence being in the Islamic tradition. Morocco, Egypt and Iran each have a university whose origins go back to the years 859, 970 and 1065, respectively. Natural sciences and religious studies did not conflict with one another at such schools.
The next universities to be established outside the Middle East were the University of Bologna (1088 in Italy) and the University of Paris (1096 in France). These later dates, however, are a bit misleading. These institutions did not just spring up without a context. The University of Bologna arose as a centre of the study of law: church law as well as Roman law . Furthermore, the places that become European universities in the 11th and 12th centuries started out as cathedral-based schools. Here bishops had taken responsibility for teaching the next generation of priests and church leaders from at least the 6th century A.D. by teaching them the Bible and doctrine but also literacy in Latin grammar. The University of Paris was anything but secular when it first opened. It was divided into four sections: Arts, Medicine, Law and Theology, but before attaining a legal, medical or theological degree all students had to complete the liberal arts course of study . In the same way, cathedral schools were also the precursor of Britain’s prestigious Oxford and Cambridge Universities.
Turning to the “new world,” Harvard was established in 1636 and the College of William and Mary began in 1693, both while America still consisted of a collection of colonies. Harvard was founded by a group of Puritans who had arrived in Massachusetts just sixteen years earlier. They recognized the importance of education for the future of the colony and its proper development. The motto they chose was “Veritas,” Latin for truth. Its first benefactor, John Harvard, died one year after coming to the new world, but he gave his complete library and half of his estate to the fledgling institution. In gratitude, it was named in his honour. The College of William and Mary’s charter said it was to be a “perpetual College of Divinity, Philosophy, Languages, and other good Arts and Sciences.” Thomas Jefferson attended this school about 70 years after its founding, and at that time all but one of the professors on staff were clergymen. That small fact indicates that higher education and Christian faith were not seen as incompatible during the years around American Independence.
In New France (now the largely French-speaking part of Canada) Jesuit priests accompanied settlers and adventurers in the early 1600’s. They established basic schools widely; within 50 years they also had a central institution of higher education to prepare young men to the Jesuit priesthood. Laval University proudly traces its heritage back to 1663 but on its public site makes no mention of the faith commitment of its first founders. Montreal’s Concordia University, founded in 1848 as Loyola College, had a similar origin. 
The oldest English speaking university in Canada is located in the Maritimes: the University of New Brunswick. It was founded in 1785, about a decade after the American Revolution by British refugees, who did not favor cutting ties with the Empire and thus moved northward. The initial goal of such a school was to give youth a “virtuous education” in the following areas: Religion, Literature, Loyalty and good Morals. It set out to offer enrolment to students regardless of the particular church denomination they might belong to, but it was largely run by Anglican-based leadership. 
Coming at last to Ontario, Canada, there are now 19 public universities to which students can apply via one centralized system. Of these, fourteen had a clear faith-based origin, as explained on the “history” section of their websites. Two examples from the nation’s capital would be appropriate even though they were founded 94 years apart:
1) University of Ottawa started out in 1848 as the College of Bytown founded by a Roman Catholic bishop. He handed over the control of the school to the society of Mary Immaculate. In 1965 this religious institution was renamed St. Paul’s University and the name University of Ottawa was given to the liberal arts program. St. Paul’s University continues to be affiliated with the University of Ottawa.
2) Carleton University in Ottawa began in 1942 and boasts being the first “non-denominational” university in Ontario. That does not mean it set itself up against faith, but that it would not favour any particular Christian background. The YMCA of Ottawa was instrumental in establishing this school at a time when “YMCA” meant more than a pool and fitness club. Young Men’s Christian Association (YMCA) was a community centre that engaged youth in integrating faith in different aspects of life.
Universities as institutions where young adults can learn specialized skills and take their place in society are highly respected in the West. The pioneering effort of churches and visionary church leaders cannot be underestimated. The funds raised to construct the first buildings did not come from government grants but from grass roots people (some of whom had wealth to share) who felt that moral and constructive learning for future generations was important. Without that heritage starting in Europe, would we really have these schools of excellence today? While most Western universities have currently shifted their focus away from faith, they would not exist at all if we had a world with no vestiges of religion.
 Gerald L. Gutek A History of the Western Educational Experience. (1995), p. 100-101 http://www.unb.ca/aboutunb/history/historicalsketch.html