Several of them are Monarchies or Constitutional Monarchies. Saudi Arabia and United Arab Emerites come to mind. Pakistan and Turkey both have secular elected governments with cyclical and varying degrees of independance from religious influences. Azerbaijan, Burkina Faso, Gambia, Guinea, Mali, Senegal, Chad, Djibouti, Indonesia, Kazakhstan, Kyrgystan, Northern Cyprus, Tajikstan, Turkmenistan, Uzbekistan, Albania, Bosnia and Herzegovina all have some form of officially secular government, elected government. Several countries in Northern Africa have no functional government or one rules by the Military.
If your meant to ask, "Which ones are not influenced by Islamic beliefs?" that would probably be none... Of course I'm not sure what that proves? Every country in the world is influenced by the beliefs of their citizens?
I really don't want to pick a fight over this, but there are muslim countries in the world that you don't see every day on TV.