What is this spider from Arizona?
It's hard to judge from a single photo but it appears to be from the Family Theridiidae (cobweb spiders). Spiders in this family have long front (first legs)and much shorter third legs as the spider in your photo seems to have. But the perspective may be off. You don't mention the size which would help.

I enjoy photographing insects and spiders in my area. One thing I found when I was trying to identify spiders is colour and pattern can vary quite a bit from different locale. Sometimes two spiders of the same species could look like two completely different species. 

So please bear this in mind. All I am is an arthropod enthusiast that has benefited from some more skilled and knowledgeable people helping me out. With that in mind, I wonder if your spider might be Phylloneta pictipes (syn. Theridion pictipes). 



Source: http://bugguide.net/node/view/2209

I should've said but the two spiders above are the same species; male on the right and female on the left.

You can check out more spiders of this species at http://bugguide.net/node/view/49080/bgimage and see how they vary.