Motto: "We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far." H.P. Lovecraft
The Usual Suspects is the obvious choice for a twist movie, the problem is that it's so famous that most people already know the twist even if they haven't watched the movie.
Other than that:
The Machinist (One of Christian Bale's most underrated performances)
A Cure For Wellness (A lot like Shutter Island but a very strange and distinct movie)
Jacob's Ladder (Weird is an understatement)
Shutter Island (Pretty sure you will have seen this)
Fight Club (See above)
Gone Girl (See above)
The Girl With The Dragon Tattoo (American and Swedish versions)
Se7en (One of the best movie endings ever)
Zodiac (David Fincher recreated The Zodiac Killer's crimes with scary accuracy, this is like going back in time so for curiosity alone it's worth a watch.)
The Prestige (Probably the best magic focused movie ever made. And yes I'm including every Harry Potter film there)
The Game (This has one of those twist endings where you'd guess it 10 minutes in as a joke and say "Knew it!" even though you really didn't.)
Wind River (Just creepy.)
Prisoners (Annoyingly great ending.)
Panic Room (One of the tensest movies you'll ever see.)
Basically anything directed by either David Fincher or M. Night Shyamalan, with the former being an infinitely better director.
Edit after LifeOfPy's post: Can recommend American Psycho, brilliant film.
Mulholland Drive, Memento, the Sixth Sense (M. Night Shyamalan's best film), the original Planet of the Apes from 1968, Black Swan, American Psycho, and the original Oldboy are some good ones that haven't been listed.
But my favorite movie twists would have to be from Jacob's Ladder (which itself is inspired from the short story An Occurrence at Owl Creek Bridge so check out the Twilight Zone episode of the same name too if you watch Jacob's Ladder), the Sixth Sense, and Memento.
And the obvious suggestion after watching Breaking Bad would be to start watching Better Call Saul, but it's still airing so there's no ending yet but definitely worth watching the 3 seasons they have out now and watch the 4th when it comes out next year. I recently finished both BB and BCS and started watching Lost again but can't really think of any suggestions besides BCS.