Turkey actually is a successful example of a democratic state where Islam is the religion of the vast majority, albeit it is not a Muslim state, as the constitution is religion-agnostic; nowhere in it exists a phrase which even implies that the state has an official religion. Current government follows a conservative policy and has been elected with roughly 49% of votes. This eventually gave them power and resources to work in an autocratical manner. They have also been able to enforce censorship and direct the media companies in the way they want. Turkish parliament has a total count of 550 members and 327 of these are members of AKP, which let's them legislate proposals even in situations where there is no support from the opposition (although they can't in some cases where the required fraction of parliamentarian votes are more that 50%, which is usually demanded by the constitution for some fundamental stuff, like editing the constitution text itself). Added the fact that the president is also descendant from this party, they apparently have a humongous authority, originating from a, so to speak
bug in election system: A party with less than 10% vote rate can not have it's members in the parliament, which eventually let them occupy more that 50% of the 550 quota of the number of parliamentarians.
The next elections will be held on 2015, at which I expect that the votes are going to be distributed even among the three major parties, where two of these are CHP and MHP, which are defined to be social-democrat-left and nationalist-concervative-right (with no apparent tendency towards theocratic ideals) respectively. AKP will probably be in the parliament, albeit lack the dominion present today.