Oh some hilarious ones..
Years ago when I had a council bedsit on a very small estate (really, just one big cul-de-sac) where most of the residents were elderly, one neighbour decided I really shouldn't live there as I wasn't old.
She spread around that I was a prostitute and a paedo on the grounds that I had young boys coming to my flat, and other older men in and out.
The 'young boys' were my friends 12 year old daughter who had a shaved head, and my own 17 year old sister who also had a very short haircut.
The men were - my actual boyfriend, my best mates boyfriend who lived downstairs (with my best mate), and a gay male friend.
At one time walking my dog around the communal garden and back street, I discovered some needles discarded by drug users - I put a couple of bricks over them and rang the council, but let a few of the neighbours who had visiting grand kids who played in that area know that there were needles so don't let the kids play there til the council have cleaned up... responsible no?
No apparently I WAS A DRUG DEALER.... K' then..
Oh and a few years ago I discovered that an ex boyfriend I'd dated briefly oooh.. 10 years earlier, and who had been happily married to someone for at least 8 years... told a mutual friend that he 'knew I was still in love with him'...
I had not spoken to him in at least 9 years!