There are literally thousands of animal shelters across the country. I can't begin to list them all, but it is possible to highlight a few, particularly one's with which we've had personal experience. More shelters will be added to this list as time permits.
Seattle
Purrfect Pals
230 McRae Road NE
Arlington, WA 98223
As the name suggests, Purrfect Pals specializes in caring for cats. The organization operates an adoption shelter as well as offering lifetime sanctuary for hard to place cats, taking in feral as well as cats with FIV, Leukemia, or other illnesses. Purrfect Pals believes in giving every cat a chance. They also sponsor the popular Average Joe Cat Show.
The Humane Society for Seattle/King County
13212 SE Eastgate Way
Bellevue, WA 98005-4408
The Humane Society is the organization for which we currently foster cats and kittens. As I'm writing this, our foster kitten "Rupert" is sleeping on my desk! We've had a great experience working with them for the past two years, and I couldn't recommend our local Humane Society enough. Most shelters are always looking for foster parents, and I'm sure they'd be glad to hear from you.
The Progressive Animal Welfare Society
15305 44th Ave. W
Lynnwood, WA 98087
In addition to providing companion animal services in its local facilities, PAWS also supports an extensive and well established wildlife rehabilitation program. If you believe you have found an injured wild animal, contact the PAWS Wildlife Center for assistance.
San Francisco
Pets Unlimited
2343 Fillmore Street
San Francisco, CA 94115
This is the first place we fostered cats. Pets Unlimited is an amazing organization that not only takes in animals, they actively seek out and rescue animals from municipal and other shelters in the Bay Area. All cats at Pets Unlimited are given a home at this state-of-the-art shelter's facilities in comfortable rooms until they are adopted, no matter how long it takes. They will take every effort to place each and every cat.
Pets Are Wonderful Support
645 Harrison St, Suite 100
San Francisco, CA 94107
Just to be clear, PAWS is not a shelter per se. What they do is assist "low-income persons with HIV/AIDS and other disabling illnesses" care for their pets. If you are considering fostering cats and kittens for a shelter, you may also want to volunteer with PAWS and help disabled persons keep the animals they love. It's a great cause that benefits people in need and helps keep pets in their own homes.
Utah
Best Friends Animal Society
5001 Angel Canyon Road
Kanab, Utah 84741-5000
This organization works to ensure that "homeless, unwanted animals are no longer being destroyed in shelters" and "every healthy dog or cat can be guaranteed a good life in a caring home." They recently helped us find a good home for a difficult to place foster cat. Working with our local Humane Society and Best Friends, we were able to find Erasmus a new family. I highly recommend getting involved with any program they sponsor.