Think of your favorite anime ability. The best parts of anime action shows are the weirdly exaggerated anime abilities that come with the territory. Goku's Kamehameha, Naruto's Rasengan, and Monkey D. Luffy's Gum-Gum Pistol are all fantastic examples of signature anime attacks that are capable of delivering a fatal blow while looking cool in the process. As powerful as these anime abilities are, they never cross the line of being too overpowered. After all, it's not a good fight if there's no struggle.
However, not every anime attack knows when enough is enough. Whether intentional or horribly calculated on the writer's part, these overpowered anime abilities break the viewer's suspension of disbelief by making their initiator appear God-like when compared to anyone else. It's like beginning a new RPG at level 100, while every enemy you face is at level one.
Saitama's superhero powers far exceed those of any anime character before him, and when forced to get serious, he's capable of producing exceedingly deadly results. When he applies actual effort - no matter how minimal it may be - he can deflect a beam powerful enough to destroy a planet like it's nothing, as seen in his fight with the alien invader Boros. Even then, his Serious Punch move that obliterates Boros isn't Saitama at full power. It's impossible to imagine the damage Saitama is capable of if he ever faced a worthy foe.
Sōsuke Aizen is already one of the smartest villains on Bleach, but his Zanpakuto elevates him to a threateningly new level. It's a powerful tool that hypnotizes its victims with a mere glance. The hypnotic move called the Kanzen Saimin completely controls the victim's five senses, causing them to misinterpret sights, sounds, tastes, feel, and smells. Even after the victim becomes aware of the hypnosis, they're still unable to break the spell. It's the perfect power for a manipulator like Aizen, who uses it both on and off the battlefield to stay one step ahead of his enemies.
It's never good to bury your emotions, but Shigeo Kageyama (AKA Mob) from Mob Psycho 100 has his reasons for keeping his feelings in check. To maintain a handle on his ever-expanding psychic powers, Mob seals them away behind several emotional locks that only break if they reach 100% fulfillment. When those emotional locks break, Mob becomes one of the most powerful psychics to ever walk the Earth. As if becoming a psychic juggernaut wasn't enough, Mob can overwhelm his enemies even more by entering ???% mode, although he can only do it while unconscious.
Super strength and speed are overrated. If you want real overpowered anime ability, it's vector manipulation. As demonstrated by Accelerator from A Certain Magical Index, vector manipulation allows the user to control the magnitude and direction of any surrounding object. Accelerator can take a bullet that's targeted at his head, and fling it back at the shooter. On top of that, the ability allows Accelerator to stop the Earth's rotation for five minutes, just to get the upper hand in battle.