If you do not pay for your traffic fine, there are multiple consequences that may occur:

Your driving privileges will be suspended by the Motor Vehicle Department and you will be unable to register or renew registration on any vehicles until all fines are paid in full. Suspensions in Arizona are honored by most states.
Your case may be referred to a collection agency. Default fees and surcharges will be added to your balance.
Information regarding non-payment may be forwarded to a credit bureau, which may affect your ability to obtain credit.
Your tax refund may be intercepted through the Debt Set Off Program via Arizona Tax Refund Interception.

FAQ - Paying a Traffic Ticket