Identification of this humpbacked, brown, clawed insect climbing up my wall?
That's the exoskeleton (shed outer shell) of a young cicada, left behind when it emerged as an adult and (we can imagine) flew off somewhere to sing, and find a mate.

This article on EarthSky has a nice description of the big cicada hatch this summer (2013), and also a great picture of an adult cicada emerging from the exoskeleton. However, this article and other recent news about cicadas mostly deals with the Eastern US genus Magicicada, and it's likely that in Arizona you're seeing a different genus (that is, a different type of cicada).

You'd probably have to find an adult in order to identify exactly what genus and species of cicada you've got. Alternatively, you could listen for their songs – this site has examples of calls from many Western US species, including the Apache Cicada Diceroprocta apache, which seems to be a common cicada in your area.