Granted I haven't seen that much anime so I'll just say what I thought was the most ridiculous
Death Note
Through some magic bullshit rule that only gets introduced at the last minute, Light is able to temporarily lose all memory of the death note and lose police suspicion on him. He then spends the next 8 episodes helping out the police in some other random bullshit crime that has very little to do with the main plot and just screams out filler material to extend the series. Also, L dying. He's hyped as the most brilliant detective in the world and is one of the most interesting characters and then gets killed. Big shock, obviously, which sets the mind racing. Has Light won? I mean, where does the series go from here, now that there is nobody to complete with Light's intellect? What's that? Oh L has a student who is also a master detective and a crazy eccentric as well and has only been mentioned now? Gee that's handy.
Also Yu-Gi-Oh. These weren't so much plot twists as it was just how the show could be at times. I was 12 and even I saw the ridiculousness that these battle sequences would happen more than once.
Yu-gi-oh: I play my dark magician which can deal triple damage to your life points!
Villian: Not so fast! My creature can automatically repel magic and deflect it back directly at you! You're finished now..
Yu-gi-oh: Except, with my special magic card which has never been shown until now I can break the rules of the game and deflect your spell right back at you! It's over!
Villian:*smirk: Except...I am now able to introduce some magic bullshit rule that allows me to play a new card never shown before which can conveniently negate your attack!