My favorite is the predestination paradox and my favorite take on this was on Robert Heinleins short story called All you Zombies. It was adapted into film and titled Predestination
(Sings Im my own grandpa in the background)
The trailer says "You will love this film". Guess they really have a time machine.

Added it to the list.
Predestination is a brilliant movie, one of my favourites actually. If you like Predestination, you'll also like Netflix's new series "Dark", it's a German language film but has been dubbed, or subbed. Either way, it's brilliant. The Man from Earth is also a good movie with a similar theme.