If your animal is a purebred, check telephone book or contact local animal control agency for phone numbers of breed rescue groups in your area. (paw-rescue.org)
I've also uncovered some harder to find breed rescue groups, but some of these pure breed cat rescue sites haven't been updated in a while. (cat-lovers-only.com)
If a specific breed is your heart's desire, search the internet for breed rescue groups. (floridawildvethospital.com)