How many US states have two or more time zones?

Thirteen. "Oregon and Idaho are split between the Mountain and Pacific time zones. Nebraska, Kansas, Texas, North and South Dakota are divided between Central and Mountain time zones. Florida, Michigan, Indiana, Kentucky, and Tennessee are split between Eastern and Central time zones. Also, Alaska is split between the Alaska time zone and the Hawaii-Aleutian time zone."

http://wiki.answers.com/Q/What_state_has_two_different_time_zones

Time in Indiana refers to the controversial time zone division of Indiana, and to the state's historical response to daylight saving time. The official dividing line between Eastern Time and Central Time has, over time, progressively moved west, from the Indiana–Ohio border, to a position where it divided Indiana down the middle, to the Indiana–Illinois border as it is today.

https://en.wikipedia.org/wiki/Time_in_Indiana