What, you don’t have a favorite? Come on, there are plenty to choose from.
I’ll start the ball rolling:
The Amazing Clay Man: His Skin is Mush! Nothing Can Harm Him!
I saw three back in the early 80s that have stuck with me all these years. Well, the general ideas stuck. I won’t vouch for the exact wording.
**JFK Alive But Brain Dead in a Secret Swiss Mountain Clinic!
Spanish Monks Have Devil Trapped in Cell!
Devil Seen Escaping in Alaskan Oil Well Fire!**
Plant People! Scientists create people from plants (As I remember)
Morgyn, I’m hardly doubting you (it is the WWN after all), but I remember a short story about the monks and the devil. It may have been televised as a Twilight Zone (or TZ-type) show as well.
Pardon my ignorance, but is this publication meant to be parody? Onion like, right?
It pre-dates the Onion and it is, well, not entirely serious, though it purports to be.
It is also defunct, I think - it was always a newsstand thing to me, especially at supermarket checkout counters. It boasted of having the BIGGEST CIRCULATION OF ANY NEWSPAPER IN AMERICA and frequently headlined articles about UFOs and ET aliens, pictures or testimonials showing Heaven/Hell were physically real locations, Elvis and Bigfoot sightings (or clonings), and (one that I saved) Saddam Hussein’s secret stash of T-Rex dinosaurs that he was planning to unleash if the US invaded Iraq.
“Underground” artist Mojo Nixon (best known for his song Elvis Is Everywhere) made a song in the late 1980s called The Amazing Bigfoot Diet whose lyrics consist solely of headlines from the Weekly World News. I love it.
The opening lines:
*
I Married A Bigfoot
I Gave Birth To My Mother
Donor Wants His Kidney Back!
Golf Cart On A Rampage
Couple Flees Talking Bear
Sleazy Pushers Are Swapping Shrunken Heads
…for COCAINE!*
It goes without saying that all of these articles were accompanied by outrageously bad mockup B&W photos. One recurring “monstrosity sighting” was called Bat Boy, who was so popular that I think he eventually started writing a column for the paper. Or at least wrote to the paper answering questions and weighing in on matters great and small.
Great googly moogly, there’s a Wikipedia page about Bat Boy!
I used to clip and save these. I’m going to have to look and see if I still have some, like the one about the BUTT-KICKING ALIENS.
See the Wikipedia article here.
It was never parody or satire, like The Onion, but in its later years it became more “wink-wink we know this is all a joke.” Earlier, it catered both to the people who read it for laughs and to the people who took it seriously (which you could if you have a very, very low credibility threshold). I think some of the articles they published had some truth to them, but they never let truth or the lack thereof get in the way of a good story.
Weird Al Yankovic’s song Midnight Star pays tribute to this sort of fine journalism.
And let’s not forget the absolutely hilarious award winning Bat Boy: The Musical.
ETA: Great googly moogly has entered my lexicon via this post. Thanks, robardin
Google books has a archived a bunch of issues for your reading pleasure(?). Here’s a good from 1988:
HE’S B-A-A-A-CK!! 600 Hitlers cloned by Russians
It’s not in the archive, but my favorite was in September 11, 2001 cover story.
Hillary Clinton has Affair with Space Alien
Bill says, "I thought she was a lesbian!"
Just the right note for a time when I needed a laugh.
Hillary Clinton Adopts Baby Space Alien!
Then, of course, the father alien endorsed Bill for president. I love it when beings from planet Zorgon get involved in our politics.
I’ll always remember the “photograph” that accompanied the
Face of Satan Seen in Volcanic Eruption
article.
Hillary names Bigfoot as her running mate!
It was shown on the Twilight Zone, but I’d never seen that episode until this year’s New Years Day marathon.
I wouldn’t be too surprised to see WWN had recycled it, as I’m seeing ads now for a movie called Unknownthat sounds suspiciously like a TWZ episode called “Person or Persons Unknown”.
They’re not printing an actual newspaper any more, but they do publish new articles online on a pretty regular basis.
I actually bought a issue of WWN a few years back with the big lead story, “Kitten Guilty of Murder!: Sign the petition INSIDE or Fluffy DIES!” which included a picture of the rambunctious scamp splayed out on a table getting ready to receive the lethal injection. (That’s the August 29, 2005 issue, if you want to hunt it down) 
Skeptic Magazine hosts a podcast called Monster Talk, check out the october 20, 2010 show.
My Dad sent a copy to his twin brother once:
MOM SELLS UGLY TWINS TO CIRCUS
I couldn’t stand the sight of them, she said
My uncle was not amused.
I saved one (might have been the National Enquirer) with the headline:
Jealous Computer Kills Top Scientist!