Presumably you are a seller on eBay, and not just a buyer, correct?
If so, then your eBay selling activities, if they amount to more than just an occasional hobby or the re-selling of older (or used) personal property that you have acquired, would be considered a type of self-employment, and should be reported on a federal Form 1040, Schedule C (but you can also deduct your expenses from income there). Of course, the state of Washington has no similar personal income tax upon which to report self-employment, or other, income. But that doesn't mean that Washington does not impose any taxes on businesses.
That said, however, your question specifically is directed at the rules for eBay (as an online seller?) based in Washington state. Probably, you want to know if you should be collecting Washington sales tax, and / or paying the state's B & O (Business & Occupation) tax. For an answer to that, we would respectfully direct you to the Washington Department of Revenue webpage where these matters are officially discussed:
http://dor.wa.gov/Content/DoingBusiness/BusinessTypes/Industry/OnlineSalesofGooods/default.aspx
If, instead, you are asking this question from the perspective as a buyer on eBay, as it relates to the paying of Washington sales tax on items purchased over the internet for which Washington sales taxes are not paid (called a "Use Tax"), then you may refer to this Washington Department of Revenue webpage for more information on that.
http://dor.wa.gov/content/FindTaxesAndRates/UseTax/
Thank you for asking about this important subject.
