This is a good handout from a the VCA Animal Referral & Emergency Center of Arizona.  Below are some of the things that are considered an emergency, and should be seen right away by a veterinarian.  Of course, if your pet is injured or ill in any other way not written below, please call a local animal hospital to see if it is an emergency. 
The Complete Pet Animal Hospital
5135 N Dysart Road Suite 4
Litchfield Park, AZ 85340
Phone: (623) 935-9632
Fax: (623) 9359764

5135 N. Dysart Rd., Suite 4 Litchfield Park, AZ 85340
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(623) 935-9632
Clinic Hours
Monday: 8 am- 5:30 pm
Tuesday: 8 am- 5:30 pm
Wednesday: 8 am- 2 pm
Thursday: 8 am- 5:50 pm
Friday: 8 am- 5:30 pm
Saturday: 8 am- Noon