Homeowners often try to use pesticides to eliminate indoor crickets, but these hardy insects don't respond well to this treatment. However, sticky boards placed strategically behind refrigerators and near sources of water will trap crickets safely. You can also simply crush any crickets you find or throw them outdoors.
If crickets are a perennial problem for you, it's a good idea to look around your home for cracks and crevices that they may be using for entry points. Seal cracks, repair window screens and ensure that your crawlspace door fits tightly to keep crickets outdoors where they belong. Trimming up bushes near the house and moving trash cans, wood piles and other hiding spots away from doors can help eliminate the cricket menace.
Several kinds of crickets are found in Arizona. Although they pose no immediate health risks (they do not bite or carry disease) they have been known to eat through everything from wallpaper glue to wool to silk.