This sounds like one of those "what color is an orange" questions. I mean, it's called the Ten Commandments, so the answer is right there, right? Ten, duh.
Turns out Mel Brooks wasn't too far off. The correct answer, according to Maimonides, is fourteen. The Second Commandment has four mitzvot (don't take any other gods, don't make idols, don't bow to an idol, and don't worship an idol in any way that does not involve bowing), and the Fourth Commandment has two (acknowledge Shabbos, and don't do any work on Shabbos.)