May I Pet Your Dog/Cat?

This phrase should always be asked of the owner when approaching an animal. If there is no owner present, avoid the animal if possible.

Look for signs

Does the animal look uncomfortable? If the animal is backing away, whining or growling, they probably don't want to be touched. Some other common signs are ears back or down, and the tail tucked between legs. If the animal approaches you, then its may be safe to pet them, but continuously reading the animals body language is very important.

Before you begin petting the animal, it is best to gradually approach them, and extend your hand for the animal to sniff. If the animal approaches you, it is a good sign that they are ok to pet. However, if there is any point when it appears that the animal is not comfortable, it is best to stop petting the animal.

Over excited dog?

What happens if a dog runs up to you, and tries to jump? If you have a kid, or you are a kid that is uncomfortable with dogs, there is a simple trick to get the dog to back down. 

Start by turning away from the dog. From there, be very still, and do not move or give the dog any attention. This is also known as "being a tree".