Muslims known as Islamists claim that religion and politics go hand in hand and any attempt to separate them is blasphemous and completely against the teachings of Islam at its very core. This is by no means a small segment of the Muslim population.
However, within Islam there is also an important movement that seeks to modernize Islamic government and separate church from state. Both movements have their defenders and their detractors and that secularism should have in a particular Muslim nation is a hotly debated issue amongst Muslim scholars and philosophers. It is clear that there are models for both types of government around the World, although the secular model has been substantially more successful in general. In fact, most countries in the world with a majority Muslim population have governments that are more or less secular.
For Islamists, the most important determinants of a nation's politics are the Qur'an and the Hadith, as well as Shariah law. Their main argument is that throughout the whole time that Islam has been on this Earth, this has been the way that things have been done. That secularism is a serious blasphemy and even a form of atheism; it is a form of rebelling against God. This is true in the sense that Muslims consider Islam to be a basic part of every aspect of their lives and, following this logic, government should be no different.
Some countries, like Iran or Saudi Arabia, claim that Islam is very clearly against secularism. They have even gone as far as passing laws or government-sanctioned recommendations that state that any other way of life that is not in line with the Qur'an or the Prophet is unlawful. These kinds of beliefs are even punishable by law. For example, stating that the laws of man are in any way better than Shariah law, or to publicly state that the legal punishments in the Qur'an (like cutting off a thief's hand) are not compatible with modernity is against the law in these countries. Even stating the notion that Islam should only deal with each individual's relationship with God and not with government is against the law.
This has been a very divisive issue amongst Muslims and Islamists have resorted to violence and even murder against Muslims that promote secularism as a positive way for Islam. It is unfortunate that this sector of the Muslim population is more interested in upholding the laws that punish people rather than trying to follow those that urge them to do no harm. The main factor holding back states that are more secular in nature in most Muslim countries are militant Islamists, many of them quite radical in their views.