I think this is awesome! Not only are shelter dogs great, if there is a certain breed of dog or cat that you are drawn to, then I guarantee there is a rescue organization for that breed. There are a lot of compassionate and selfless people out there that rescue their "breed" from shelters, then foster them and find their forever homes. Just google your breed/rescue and see what you find.
My sweet Wendy was rescued from a puppy mill and fostered by the Fox Terrier Rescue folks. She was passed to us by her guardian angel Lydia.
We have been her forever home for about 7 years now.