Businesses are formed in states other than their owners' states of residence all the time. However, it seldom makes sense to form a business in a state that you are not operating in. Even if you form your company in Washington, if you are doing business in Oregon and/or you live in Oregon, you will most likely have to register your business in Oregon and pay Oregon taxes of one kind or another.
I agree with the previous answer. You can form your business in any state you want, as long as you have a "registered agent" in that state. However, you are required to register your business in every state you do business in. This means that if you are a Washington IT company doing consulting for companies in Oregon and California, you are "doing business" in California and Oregon and will be required to register your business with those states. Once registered, you will be responsible for the various business taxes associated with doing business in those states.
There are other considerations for choosing where to form your business, and it'd be best to talk with an attorney about your objectives for your business in order to determine the best choice of entity and location for forming your business. It's always best to have the right foundation for growing your business.
No problem. Use a Business Law attorney and select a Registered Agent in the other State. Good Luck in your new business !!