These answers all should work... except when they don't: it often appears that there is nothing to select or that when you do select the watermark in a header... it does not appear that it is selected. Moreover, sometimes "delete" or "backspace" to not work. Having had this occur many times my solution set is:
First, try going to the Page Layout ribbon, Watermark drop down and select "remove watermark." If it works, good for you. If it doesn't, join the crowd.
Watermarks are stored as part of the header in each section and may vary from section to section in Word. You will know if you have multiple sections if some pages have watermarks and some do not. If you show hidden characters and there are rows of double dotted lines (Word's representation of a section break) then you have to work each section with a water mark. Removing watermarks should be easy as indicated above. Unfortunately, often as not, its not to be. So:
1. Double-click inside the FIRST PAGE of each section containing your offending watermark. This opens the header. You think all the "header" stuff is in the text-box. Its not, the water mark you can not get rid of is halfway down the page where you see it... and below the headers end-of-text box indicator... but its actually in that header. So, to delete it, you have to open the header and then work what appears to be below the header.
2. Move your cursor over some of the letters in the watermark until it turns into a 4-way arrow (NOTE, it may NOT turn into a 4-way arrow and that is NOT unusual... just not the way it should work... so even if it doesn't turn into a 4-way arrow, put your cursor over the offending watermark anyway.
3. Click to select the watermark (you MAY see selection handles around the watermark graphic when it's selected) (NOTE, it may NOT show selection handles around the watermark or otherwise appear as if its selected... gotta love MS WORD... if not, do not give up hope and with courage proceed after clicking once on the offending watermark... in most cases while Word does not indicated the watermark is selected it really is and the rest of these instructions will work).
4. OK... 3 different things to try in this order:
4.a Press the DELETE key to remove the watermark. Ah-ha you say, that didn't do it. Hey, this is MS Word. If it were easy you wouldn't be here.
4.b. Try the same thing, select by clicking on it and then pressing BACKSPACE key. Ah-ha you say... still doesn't work and this guy doesn't know what he is talking about! Maybe, and that is when the non-worthy quite. But remember, MS WORD is your problem... not me. Soooooo....
4.c. WHEN THE WM DOES NOT APPEAR TO SELECT OR DELETE: Try again to single click on the offending water mark (to select it), right click (Mac users control-click) to get a contextual menu... but you must first select the graphic even it it does not appear selected in order to get the correct contextual menu, and select <CUT>. For me, this has always worked EVEN WHEN IT DOESN'T APPEAR TO WORK... be of stout heart and...
5. Save and close your document. Count to "3". Open it back up. If I'm worth your time, your water mark will be gone regardless of what you thought was/wasn't happening.
For me, this has worked every time on multiple platforms, various OS's in both the corporate and a home environment. Yes, there are a couple of steps you have to take on faith because at different times they may not appear to be doing anything (like when you try to select the watermark, or you say cut... but its still there... follow through).
Two more thoughts... if none of the above works (in which case you may not be doing something exactly right.. but instead of getting (more) frustrated, try either of the following "inelegant solutions":
A. Go into the header and select the watermark and change the text fill to "no fill" or white: if on white paper/background it will work but this is really ugly because remember, you didn't really get rid of it, you just made it not show under certain (white paper) conditions).
B. MS Word also has under the MS Suite "logo" a Prepare>Inspect Document feature that when run, will identify if there are watermarks and offer to remove them. Problem is, it will remove headers and footers at the same time... but usually it is not too difficult to replace them (especially if you remember to copy and paste the text you need somewhere else so you can simply copy it back).
Hope this helps.