Daylight Saving Time - for the U.S. and its territories - is NOT observed in Hawaii, American Samoa, Guam, Puerto Rico, the Virgin Islands, and by most of Arizona (with the exception of the Navajo Indian Reservation in Arizona).
Indiana, which used to be split with a portion of the state observing DST and the other half not, is now whole. In the past, counties in the Eastern Time Zone portion of the state did not observe DST. They were on standard time year round. A state law was passed in 2005 that has the entire state of Indiana observing DST beginning in April 2006.
Indiana isn't the only state that wanted to change daylight saving time. California asked for federal "approval" to move to a "year-round" Daylight Saving Time in 2001-2002 because of its energy crisis.
According to Mining Co. Guide to Geography, DST is also observed in about 70 countries:
"Other parts of the world observe Daylight Saving Time as well. While European nations have been taking advantage of the time change for decades, in 1996 the European Union (EU) standardized a EU-wide "summertime period." The EU version of Daylight Saving Time runs from the last Sunday in March through the last Sunday in October. During the summer, Russia's clocks are two hours ahead of standard time. During the winter, all 11 of the Russian time zones are an hour ahead of standard time. During the summer months, Russian clocks are advanced another hour ahead. With their high latitude, the two hours of Daylight Saving Time really helps to save daylight. In the southern hemisphere where summer comes in December, Daylight Saving Time is observed from October to March. Equatorial and tropical countries (lower latitudes) don't observe Daylight Saving Time since the daylight hours are similar during every season, so there's no advantage to moving clocks forward during the summer."
Daylight Saving Time - Saving Time, Saving Energy (interesting article by California Energy Commission)
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Blue: Areas that observe daylight saving time
Orange: Areas that once observed daylight saving time
Red: Areas that have never observed daylight saving time