Rescue a shelter animal. Shelters are generally over crowded and average 10 new animals a day.
Adopt a foster animal. They are taken from the shelter and brought into a foster's home for socialization and vetting before adoption.
If CCAC or CCHS doesn't have what you are looking for, then check out this site. You can simplify your results by searching for the breed, sex, age, type of animal, and what's near you.
The Humane Alliance Spay/Neuter Clinic has been making a tremendous impact on the animal overpopulation problem in the region since the spring of 1994. William H. McKelvy founded the organization with the mission to provide low-cost spay/neuter services; the non-lethal, responsible solution to pet overpopulation. What began as a local effort escalated into a regional endeavor.