Oh, let's see
Four Peaks: I love Four Peaks. Four Peaks is in Tempe, and is AZ's biggest brewery, and IMO the best. Kiltlifter is their flagship brew. It's one of the better Scottish Exports i've ever had, and has really caught some traction in bars and grocery stores all over the state in the last couple years. They also make a fantastic English best bitter (8th street ale), and one of, if not the, best IPA i've ever had (Hop Knot). It's extremely floral and citrusy without being too bitter (about 47IBU). I absolutely love that beer. All their beers are well balanced, and consistently great. The brew pub is a cool atmosphere, built into an old 19th century brick warehouse. And the food is really, really good. (The carne adovado will knock your socks off. Actually pretty much the entire menu is killer, including the specials.) If you only have time for one, go to four peaks.
San Tan Brewery: San Tan is down in Chandler, and pretty new(opened in 2007 I think). They have a pretty cool little brew pub in the historic distric of Chandler. They make a good Pale ale (Devil's Ale), a good IPA (HopShock), and have a great seasonal winter warmer on tap right now. Food is pretty good, but I still favor Four Peaks kitchen. Good beer though, definitely worth the stop if you have the time. They also have some awesome tulip glasses that are mouthblown, and made for them by the glass shop down the street. They're pretty sweet.
Nimbus Brewery: If you're going to hit a brewery in Tucson, Nimbus is a must. Great beer. I've only been once a couple years ago, so I don't remember too many details, but I remember both their blonde, and their stout being fantastic.
Papago Brewery in Scottsdale is pretty good. They have lots of regonal micro-brews on tap other than their own beers.
Sun-up Brewery: I hate to admit, but I've never made it up there, although i've been meaning too.
If you ask me, Four Peaks and Nimbus would be the two must visits. San Tan, if you can find the time.