I live in WA State. My neighbors are building a deck all the way to our shared fence. Can they legally do this?

In order to answer this question, you will need to contact
your local government.  You will need to talk to someone in whichever department deals
with issues of zoning and building.  This department can have different names in
different jurisdictions.

The reason that you will have to
do this is that issues of setbacks (how far from a lot line a building can extend) is
different in different cities and can even differ from zone to zone within a given
city.  For example, in the city where I live in Washington State (and where my wife is a
city planner who is involved in such things as zoning and setbacks), there are four
different types of residential zones and they do not all have the same amount of
required setback in a side yard (I assume that the deck is coming up to your side
fence).

As you can see from href="http://clerk.seattle.gov/~scripts/nph-brs.exe?d=CODE&s1=23.47A.014.snum.&Sect5=CODE1&Sect6=HITOFF&l=20&p=1&u=/~public/code1.htm&r=1&f=G">this
link, the deck that you describe would probably be illegal in Seattle.  But if
you live in some other city, the law could well be
different.

So, please do get in touch with your local city
government.  Ask them about the rules that govern setbacks.  There will be someone in
the zoning department who will be able to give you information that is accurate for your
specific property.