That answer would be Yuma, Arizona, which averages a paltry 2.65 inches of rain per year, and that probably comes on about five total days. Las Vegas checks in a No. 2 with 4.19" a year, while Bishop and Bakersfield, California come in at just over 5 1/2 inches. Phoenix rounds out the top five with 7" of rain a year.
Around Western Washington, Sequim is a good bet, averaging just 18" of rain a year due to the Olympic Rain Shadow. Although after being at sea for nearly 10 months, I'm sure many wouldn't be phased if there were a few raindrops around here.