A wheel that isn't broken needn't be reinvented. If used too long, however, it tends to creak and lose its appeal. One can say the same thing about anime powers, particularly in the shonen genre. Powers are pretty much like story plots, use enough varieties of them and one will likely run out of novel ones.
It's safe to say most fighting or battle anime these days resort to cliched powers. Because coming up with a new one is pretty taxing on the old grey matter. Pretty soon, some characters will start looking similar all because they share the same power. Comic books also have the same issue, what with all the homogenous superheroes. This is such a common occurrence that you can probably name plenty of characters based on these powers.
10 Superhuman Physical Traits
Enhanced strength, speed, dexterity, senses, reflexes, endurance, durability, martial arts skills, etc. If the rest of the powers in this list are common, then these traits are ubiquitous in anime. From cooking shows to superhero anime, superhuman abilities are almost mandatory.
This was likely popularized during the emergence of Goku and friends back in the 1980s. Since then, plenty of anime protagonists and villains have employed superhuman traits one way or another. Some, such as Jujutsu Kaisen, even managed to sneak it in where some characters magically started becoming stronger, faster, or tougher as an added bonus to their sorcery.
9 "Elements"
Water, earth, fire, air. Long ago, these four "elements" concocted by Greek philosophers have since been debunked thanks to science. Anime doesn't care. Maybe add lightning too if some showrunners feel like adding in a cool character with spiky hair and an energetic attitude.
Out of all those elements mentioned, fire is one of the most popular and represents its wielder's key personality. There's plenty of them in the same vein; Uchiha Sasuke from Naruto, Natsu from Fairy Tale, dearly departed Kyojuro Rengoku, and even villains who are arrogant and capable. Meanwhile, tamer and more collected characters get relegated to other elements.
8 Time & Space Control
A couple of decades ago, an anime character being able to control time or having telekinesis would have been considered unique. Now, they're either villains or overpowered and smug side characters like Satoru Gojo. Dio Brando is another notable example.
Apart from those two, some characters can also manipulate space by teleporting or creating some portals. In many anime with fighting, viewers can probably bet that there's one character capable of doing any of those powers mentioned. They also tend to be elitist or conceited.
7 Regeneration/Immortality
What good is being able to attack with the power of a thousand suns if one dies like a fly to a swatter? That's why this superpower exists both in anime and comic books. It's a pretty old and ageless perk to have and some anime even make the plot revolve around it.
It's a handy ability: if a character's hands get severed, they can grow another one in varying time periods. There are milder examples such as wounds healing faster than usual and more extreme ones more suited for vampires, such as the ability to regenerate from a speck of blood. Truth be told, it makes fights more interesting.
6 Transmutation
Transmutation or creating material out of something else— sometimes out of nothing, also used to be more unique. Nowadays, every other anime character seems to have this ability to a certain degree. Be it creating swords out of energy or making projectiles out of blood, it's quite a deadly ability.
What does set it apart from other anime powers is that it has to have some solid rules so that it doesn't invalidate its world's logic. Fullmetal Alchemist based its whole story on its transmutation or alchemy rules and it turned out well.
5 Shapeshifting
This would have fallen in with the superhuman physical traits but it's way too prominent on its own and has tons of nuances. It's also not limited to organic characters, some mecha or robots have shapeshifting capabilities either— best not to question how their mechanisms work.
Meanwhile, werewolves, vampires, and some other anime characters who sacrificed their throats shouting too much are very much eligible for this power. Shapeshifting is quite the threshold too. For some characters such as those in Naruto, it can even act as a rite of passage or indication that the transformed character is now ready for their big boy move (or big girl).
4 Illusion Manipulation
Of course, there are also those who can't match other characters' physical capabilities or special traits. Hence, they end up tinkering with the light and the atmosphere to create some treacherous illusions. Naruto even has a dedicated discipline for this power called genjutsu.
Bleach also introduces lots of characters with this kind of ability. Anime that take place in a fantasy world and with its own magical system is also quite guilty of overusing this power. Viewers might even often see protagonist trials and that run on illusion.
3 Power Nullification
Why have all these flashy powers when one can simply have the power to shut them off? Some anime characters love to even out the playing field by removing what makes nearly everyone around them special— assuming they get too close.
Power removal or nullification is another one that's starting to become common these days what with anime like My Hero Academia or Bungou Stray Dogs. It does shake up the power hierarchy by a lot so its prevalence can be excused.
2 Energy Projection
Who needs muscles and equipment when one has the power of an ion cannon at the tip of their fingers? Condensing "energy" and then shooting it into a projectile is thus a pretty widespread power. The most notable usage is probably from Saiyans and their Kamehameha waves which can decimate whole navies or even planets.
That's the most exaggerated utility for such a power. Others are more subtle and simple provide the character with visible light auras that make them look like MMORPG characters that spent too much money on cosmetic upgrades. Pretty flashy though.
1 Friendship
This is so regular in shonen right now that it's not a joke anymore. Friendships can and will boost a character's fighting spirit and capability ten-fold on average. That's a proven truth. In the heat of battle, when a character is starting to lose, all they have to do is reminisce a bit about their friends (because their parents and siblings are absent, most of the time).
Doing so will either provide them with a second wind or a blinding radiance that will shock their enemy. Their enemy (usually villains) will then be weakened at the thought of their incapability to form non-toxic relationships and their lack of friends. It goes to show that maybe the real anime power is the friends we make along the way, quite literally.