Veg Seattle no longer maintains a list of Markets and CSAs, but the Puget Sound Fresh page is a comprehensive resource on local and sustainable agriculture around Puget Sound. For more information on sustainable community agriculture, see the link below to Seattle Tilth. The links in the sections below can also help you find exactly what you're looking for.
There are many farmers markets in the puget sound area. Some of are open only seasonally, while others remain open all year long. See the link to Puget Sound Fresh below for a comprehensive list.
Community Supported Agriculture (CSAs)
In addition to farmers markets, another way to get fresh, local produce is from independent farms and CSAs (Community Supported Agriculture). These services typically offer a bin or box of organic, locally-grown produce delivered to your door on a weekly or bi-weekly basis.