With pets, emergencies happen fast. They may require immediate treatment after eating something they weren't supposed to, getting hurt by something in the house, getting bit or stung by an insect, coming in contact with something they're allergic to, swallowing a foreign object or substance ... the list goes on. Not to mention the fact that pets can't speak your language, so you won't always know what's wrong. That's why it's a much better idea to have a certified vet on your speed dial to help you through a crisis when it arises. And they do arise.
With this in mind, it is also a good idea to keep a health calendar of your pet and familiarize yourself with its habits and physical characteristics. This makes it much easier to determine that something is wrong if you see your pet exhibiting behavior that is out of the ordinary, or if you find a strange bump on its body that you don't remember being there before.
Know your pet and know your vet. You may be thankful for those precious few minutes you saved by keeping the doctor's number nearby if an unfortunate problem ever arises.