I don't know a lot about GIS history in Washington State but here is what I do know from my experience working in and around the Puget Sound area:
I remember hearing at a conference that the Washington Dept. of Natural Resources was the first ESRI GIS software customer in the state. If my memory serves me right this was in the early 1980's when the ArcInfo software was in its first version or so.
Mason County started it's GIS program around 1999. The county purchased it's first GIS software using grants. The county's GIS program started in and is still housed in the Public Works Department. In late 2004 the department came under new management and took off in another direction. In 2005 the county created a robust new roads layer and began to map the parcels for the remaining areas of the county. The parcel mapping was finished in early 2007. The county also released their internet mapping website in June of 2006.
The City of Snoqualmie started it's GIS program in 1999. The city started the program by hiring ESM Consulting Engineers of Federal Way to implement the project. ESM then shortly after hired me to do the work. I continued working and building the city's GIS system until May of 2005. The City is currently in the process of hiring it's first GIS analyst.
That's what I know off the top of my head. I'd be interested to hear what other know. Thanks!