Which states have more than two climate zones within their borders?

That's a fairly long list.  Here are some, just in the western half of the country. 

Alaska, Washington, Oregon, California, Nevada, Idaho, Utah, Arizona, Montana, Wyoming, Colorado, New Mexico, South Dakota, Nebraska, Texas.

There are also two climate zones in a number of states in the eastern half of the US.  States such as Missouri, Illinois and Indiana have a continental moist climate zone in their northern sections and humid subtropical in their southern sections.  Florida is mostly humid subtropical but the southernmost part of the state is tropical.  You can find maps that show the climate zones across the United States.