What are some films with a huge twist?

I love the film The Skin I Live In. It’s one of the best films I’ve seen. For anyone who’s seen it, you’ll know it’s got a mind-blowing twist in the plot. For anyone who hasn’t seen it, I won’t spoilt it for you – but I thoroughly recommend watching it. It is brilliant.

I’d like to check out some more films with huge twists in the story. So, what are some movies with twists?