Today is, statistically speaking, the best chance of the year you have to get by dry. In the last 110 years, it has only rained 9 times on July 22.
But if you missed today, don't worry. You've got three other chances. It turns out July 30, Aug. 1 and Aug. 4 also have had only 9 rainy days. But pretty much any day the last week in July and first week of August is pretty safe. That's why SeaFair events are held that weekend.
Although if you absolutely need dry, head to Salem, Oregon on July 12th. It has never rained on that date in their recorded weather history.
You can see the whole year's chart on the link on the left side where it says "Odds it'll rain chart"