Looks like for Washington you need to complete a couple of tests, fulfill the requirements for NBPTS certification, and have a Bachelors in the field you are looking to teach for high school.
http://www.k12.wa.us/certification/Teacher/teachertesting.aspx
The only strange thing with viewing the website is trying to figure out the Highly Qualified Teacher requirement thing. I'm guessing this is what you are referring to? The website, along with the requirements, seem a bit more convoluted than other states.
Ok, let's try to clear it all up. The information you linked is correct, but you're not looking at the requirements for those things.
There are multiple paths to certification in most states. Professionals can often start teaching while obtaining their certificates, shortage areas grant exemptions temporarily, etc.
In WA there are two major levels of certification: Residency and Professional.
For the Residency certificate you must have a Bachelors or higher, and complete the teaching certificate program, which is roughly 60-70 quarter credits, or 45ish semester credits. If the person obtains their degree IN education then those credits are included, but the total number of credits for the degree is slightly higher than usual since there are state general ed requirements on top of the certification program requirements. Furthermore they will find themselves lacking the endorsement requirements if they're going to teach secondary level. That's why most teachers either get a bachelors in education and a masters in their subject area, or vice versa.
Your residency certificate hangs in limbo until you complete more than 2 years teaching, at which point it gains a 5 year expiration date. Within that period you must obtain the professional certificate or get a special extension or exemption.
To obtain the professional certificate you must complete yet another program, this time it's about 15 quarter (10 semester) credits plus a professional portfolio and a bunch of other hoops to jump through. A masters in ed or masters in teaching program generally includes these requirements (however, as of 2011 the rules are changing to be even more strict, but less geared towards formal degree programs).
Now let's talk endorsements. In order to teach at the secondary level you have to have an endorsement on your license in your field. To receive one, you have to complete a set amount of specific classes, about 60-70 quarter (45 semester) credits. If you have a degree in your field you'll obtain most of them along that route, but there's usually at least a few additions. If you obtained your degree in education, rather than your field, then the entire body of classes will have to be taken to get your endorsement. You must have this endorsement for EVERY subject you want to teach. Want to teach History and English? You need 90 semester credits just for your endorsement then.
Then there's things like highly qualified - a NCLB requirement that a certain percentage of teachers at a school have at least a bachelors in every field they wish to teach, as well as demonstrate competency in that field through a test program. This is a national requirement, and 95% of all teachers meet the requirement.
National board certification is a resume padder that's quickly becoming almost a requirement. About 40% of teachers are national board certified, and that carries with it about 6-12 semester credits.
In every five year period a teacher must log an additional 12-15 credits of ongoing education as well. Those additional credits are included in most Masters programs, and so get the teacher out of it for the first five years.
As for the tests, they're not hard. The WEST-B is about a sixth to eighth grade general academic knowledge test. The WEST-E (PRAXIS) is basically a comprehensive final covering your subject area (ie a test about everything you learned in 4 years at college studying a subject). It's a bit intense in spots, but nothing worse than the LSAT if you bothered to learn your material.
So, yes, there's no specific requirement for a Masters degree. However, for secondary education you must have a 4 year degree in every subject you'll teach, a teaching certificate program alone or as part of a degree (about 2 years), some extra credits in every subject you teach, and within five years you'll be needing an additional year to year and a half. If you really want to get all that as isolated credits, go ahead. But 99% of the teachers get a Bachelors, and a Masters.
For Primary education you get it easier. You don't have to worry about the WEST-E, the endorsement requirements, etc. It's still very common to end up with a Masters since after 10-15 years you've already been required to complete enough credits to earn one anyway.
From what I've seen it's safe to say that roughly 50-60% of teachers have their Masters at any given time. You can spend an evening googling and find out this is supported by available data.