How come New Mexico seems to be so lefty and pro-Chicano whereas Arizona is basically apartheid South Africa?
Is it demographics or is it history?
Basically, what other people have said. But, here's a far more reaching answer I stole from someplace else.
Phoenix drives the state's politics. There's a fair amount of old money in Scottsdale and a fair amount of new money there and in Paradise Valley. (Both of these are suburbs of Phoenix). There are a couple of demographic trends driving the Phoenix area's conservatism:
1) Conservatives from Orange County, CA and other conservative parts of California see Phoenix as a reasonably-priced alternative to their current homes. Lots of people in Phoenix emigrated from California. So many, in fact, that AZ natives sometimes display "NotCal" stickers on their cars. (This is a play on NorCal, which is something I guess Northern Californians put on their cars). Land and houses are dirt cheap in Arizona compared to, say, southern California.
2) There are a whole lot of Mormons in Arizona (5-6% of the population statewide). It's an oft-repeated truism that the greatest concentration of Mormons outside of Utah is in Mesa, AZ, a Phoenix suburb. There really are a lot of Mormons in Mesa, so their political power is concentrated. Mormons (or LDS, as they often prefer) tend to be pretty conservative, politically speaking, but as with any group, there's a wide range of opinions.
3) Most people in Arizona moved there from somewhere else. Arizona has long had a reputation as a libertarian and/or conservative place, so it tends to attract people who find those things attractive.
4) Arizona has a libertarian history and a "low" tax burden. Barry Goldwater was from Arizona, for example. Fiscal conservatives tend to be really tax-averse, and so tend to move to places with low tax burdens. I put "low" in quotes because I didn't find taxes to be especially low. Property taxes were very low (and the schools reflected this, IMHO) but sales tax is effectively 9.5% in the Phoenix area and 8.5% elsewhere. Also, while local government is weak and hands-off, homeowners' associations (HOAs) tend to be pretty strong and demand annual fees.
It seemed to me that although Arizona is perceived as a low-tax, small-government paradise, taxes aren't all that low and HOAs collect revenue and act (in some ways) like an unelected strong local government.