Suppose you asked an insurance company for a letter. The insurance company kindly sent it as a PDF attached to an email. Sensibly, they protected that PDF with a password which they told you over the phone. You wrote it in a notebook and then left the notebook at work over the weekend.
How could you read the letter in the password-protected file at home, then? Remembering that the password was definitely an English word, and all in lower case, a dictionary attack has got to be worth a try.
Linux provides some handy tools for this. There’s a list of English words in /usr/share/dict/words, and a suite of PDF tools which can attempt to open the file using a password, indicating success or failure. A few minutes with Python and:
#!/usr/bin/python
import os,sys
wf=open('/usr/share/dict/words','r')
while True:
word = wf.readline().strip().lower()
if word == '':
print "No solution found"
break
print word
cmdline = 'pdftotext -upw "'+word+'" '+sys.argv[1]
result = os.system(cmdline)
if result == 0:
break
The same thing must be possible in a more hipsterly fashion using awk, but I couldn’t be bothered to figure out a sufficiently baroque command line.
By the way, the password was ‘orange’. Don’t tell anybody.
martinjonestechnology 
Or, you can simply print to file as an XPS file using the MS XPS printer built into Windows, then convert the file to PDF, it will then not be password protected. Requires Acrobat full version.
You can’t do that if the file is password-protected in the first place so you can’t even open it. Once it’s opened, you can use that technique to product a non-password-protected version, I agree.