Indeed, I believe it is a central tenet of Islam. Whether most Muslims believe it or not is another matter (most don't).
In short, this verse from the Quran sums it up pretty well (http://quran.com/9/5):
"And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. But if they should repent, establish prayer, and give zakah, let them [go] on their way. Indeed, Allah is Forgiving and Merciful."
This shows that Islam calls for death of non-believers or it requires conversion — "repent, establish prayer, zakah (basically Islamic tax)". I said subjugation because the Quran does allow for non-believers to live as long as they are subdued and pay the tax (http://quran.com/9/29).
If any would argue that this is not relevant, you must first understand the Islamic doctrine of abrogation. This surah was chronologically the second-to-last surah, and therefore it wins in any dispute or contradictory scripture.
Again, most Muslims don't believe this. But according to Islamic law what I said holds firm.