Nobody seems to have mentioned these:
Mount Lemon (southernmost ski resort in North America) near Tucson; it's open as a day hiking area in the summer.
Cochise Stronghold and Fort Bowie, in the Dragoon/Chiricahua mountains in SE AZ.
The Painted Desert and Petrified Forest East of Flagstaff
Monument Valley.
Hoover Dam
Roosevelt lake along with the three smaller lakes below it.
The London Bridge (and boardwalk) at Lake Havasu.
Day trips on the lower colorado (start at Lake Havasu or near Kingman, up or down from there, great in the Winter, mild and relaxing).
The Verde Canyon Railroad, a fine day-trip.
The former route 666 (now 393, originally the "Navajo Trail"), runs through some very spectacular scenery in AZ and NM, and makes a nice 2 day trip (plan well, there aren't a lot of cities on that road).

Closer to home there are literally hundreds of popular (and not-so-popular) places, including:
Out of Africa
The Phoenix Zoo
The Desert Botanical Gardens
The Heard Museum
Hall of Flame Museum (firefighting museum)
Arizona Railway Museum (http://www.azrymuseum.org/)
Desert Wolf Tours (http://www.desertwolftours.com/)

Many popular attractions have special events at various times of the year, so check their websites.

Josef Lowder wrote:
> What are the most fun things to do in Arizona?
> I moved here from Washington state  8 years ago
> and while I am now aclimated and glad to be here,
> I do miss all of the incredible variety of things that
> we so much enjoyed doing in Western Washington.
> When we have guest from out of town, I am hard
> pressed to think of things to suggest.
> 
> So, what do you good plug friends recommend?
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