The Humane Society is the organization for which Robert and I currently foster cats and kittens. We have been volunteering with them for about two years now, and we're happy to recommend the Humane Society as a great resource. The Society has quite a long track record, having been founded in 1897, and is very likely the oldest animal welfare society in Washington.
They offer a range of services, including adoption (of course), a boarding kennel, limited veterinary care, dog grooming, support for pet owners coping with AIDS, and training classes amongst others. The main campus is located at 13212 SE Eastgate Way in Bellevue near I-405 and I-90. It's an easy drive (traffic willing) over the bridge from Seattle. The other facility, focusing on cats and other small animals, is the new Redmond Adopt-A-Pet Center located in the Redmond Town Center, 16495 NE 74th Street in Redmond. In addition, the Humane Society frequently offers pets for adoption at various temporary locations in what you could call traveling adoption centers, including pet supply stores, around the area.
Becoming a foster parent for the Humane Society is easy, and they provide basic information as well as a volunteer application online. Being a foster parent is a very rewarding experience, and the staff members are always happy to work with you at the level you are able to participate. While it does take some commitment and a little bit of work on your part, the appreciation you can see in your foster kitten's eyes make it all worthwhile.