How many time zones are there in the continental United States?

Five

The 48 contiguous States have four zones (Eastern, Central, Mountain and Pacific). Alaska, which is also on the Continent, has a fifth time zone.

Eastern (GMT - 5 hours), Central, Mountain, Pacific, and Alaskan. Hawaii is situated in yet another time zone which is two hours earlier than pacific. (GMT -10 hours)

There exists some "sub time zones" as well.

"Arizona does not observe Daylight Saving Time. This means that in Arizona we never change our clocks like most of the rest of the country does. Other areas in the U.S. that don't observe Daylight Saving Time are Hawaii, American Samoa, Guam, Puerto Rico, the Virgin Islands. In Arizona, we just don't need another hour of sunlight!"

http://phoenix.about.com/cs/weather/qt/timezone.htm