Washingtonia is a genus of two species of fan palms from the southwest US and Mexico. Despite the name, they are not actually native to Washington State; rather, they are named after George Washington.
W. robusta, native to Baja California, is by far the most common species, since it grows faster from seed and is generally considered to be easier to grow. However, in the climate of the Pacific Northwest, it can always be relied upon to lose its leaves at temperatures around -6°C/21°F or sometimes a little higher. Fortunately though, a well established specimen will always bounce right back after being defoliated as long as it doesn't get too cold. But it will die outright at temperatures around -9°C/16°F in our climate (though, in eastern Washington where it is drier, it can tolerate somewhat colder temperatures). So there is really no place in the Pacific Northwest that is quite mild enough to grow it long term north of Curry County, Oregon. But people try it frequently anyhow, since it is very fast growing, easy to obtain cheaply, and fun to grow, and will look substantial for a few years until a hard freeze comes along.
W. filifera is the other species; it is native to California, Nevada and Arizona. Although it is much hardier than W. robusta, it too loses its leaves in our winters (even relatively mild ones, sometimes), and it is never successful because unlike W. robusta it will not survive very long if it loses its leaves frequently. It has been known to survive temperatures as low as -25°C/-12°F in very dry climates, but with wet winters and little summer heat it is nowhere near as hardy. One fellow in Oklahoma City was growing some; his venture seemed initially successful but even with all the summer heat the palms suffered after losing their leaves in the cold too often.
The best shot at growing Washingtonia in our region is probably in the driest areas, with the warmest winter temperatures and most sunshine. Who knows, perhaps W. filifera would grow in a sheltered garden in Port Townsend. W. robusta, being more moisture tolerant, might have as good of a chance in the milder parts of the Seattle area, at least anywhere Cordyline australis can survive the colder winters. So far though, no luck.
Washingtonia is probably the easiest palm to grow from seed; it has a very long shelf life and usually sprouts in a couple weeks to a month without bottom heat, and it is not succeptible to common problems such as rotting, damping off or fungus gnats. Plants should be sited in full sun and given excellent drainage for the best possible chance of survival.