The short answer to this question is "it depends".  If you are the purchaser of the home, yes you can inspect the house yourself.  But why would you want to?  I compare it to the do-it-yourself root canal.  It is possible, but not recommended.  On the other hand, if you have a friend or relative who is "handy" and you want them to "look" at the house, it may be illegal.  Home inspections are regulated in the State of Arizona and anyone who performs one is required to be licensed. 

A qualified licensed home inspector has been properly trained and has shown proficiency in the practice of home inspections.  They have the tools and experience to spot problems that the casual handyman will most likely miss.  Besides, the fee for an inspection is minimal when compared to the cost of a home, and one minor repair will usually cost more than a home inspection.  It is better to have an unbiased professional help you evaluate your potential purchase.  You will then be better able to make an informed decision and avoid unpleasant surprises in the future.