Legal Question in Landlord & Tenant Law in Washington

It depends. (sorry it always does). If the stuff is "abandoned" (boyfriend has no intention of returning and claiming the items) then it's yours. If he saddled you with some debt (e.g. he always paid the electricity bill, but didn't the month he left) and the belongings can fetch some money (don't sell the sentimental stuff of no value for purposes here) you could offset that debt by selling.

In short, there is no clear answer, but whatever the definite answer is it would not have a definite time frame. At worst you would need to hold them for a "reasonable" time, whatever that means.