We put this in 'offbeat' rather than 'news' for a very good reason.
1. Daily Mail: Sandwiches

Full story here.
2. Daily Express: The madness of human rights

Full story here.
3. Daily Star: Black-eyed ghost children

A theme that recurred.

4. The Sun: More devil children

More here. The Sun later admitted it had made a mistake with this one.
5. Daily Mirror: The new plague of rats

Full story here.
6. New York Post: The voyeur

Full story here.
7. The Toronto Sun: Mayor on crack

Full story here.
8. The Courier Mail: Obesity warning

However wonderful they all were, none, sadly, could beat this from 2011:

And yes, it really happened
More: [14 Daily Star headlines that were actually mostly true]10