There are many non-legendary Pokemon that have been very succesful in the game and have become popular among the community. Some of them even outclass some Legendaries. There are many of them that can enter the list, but only 10 made it here.
Number 10: Dragonite
Dragonite was always a very popular Pokemon, but the update that introduced abilities made it even stronger. Its ability, Multiscale, enables it to endure the first hit it takes, allowing it to use Dragon Dance one or two times. In this way, the Dragon/Flying Pseudo-Legendary can become a very powerful Pokemon that can be useful for Elite Four and PvP.
Number 9: Gengar
Gengar is one of the most common Pokemon in the game, because Gastly, its basic form, is incredibly easy to find. In fact, every player has a Gengar. Its powerful STAB attacks, its speed and its ability, Levitate, make it a very powerful option and a great choice for a sweeper. Its Mega form makes it even more powerful, even though it lacks the Shadow Tag ability.
Number 8: Alakazam
Similar to Gengar, Alakazam is a great Gen I Pokemon. It has a great movepool, great stats and massive power, enough to sweep a team after some Calm Minds. Mega Alakazam has massive power with its 170 Special Attack stat and a great 135 Speed. In conclusion, Alakazam was always, and it will be forever one very popular Pokemon.
Number 7: Gardevoir
The Fairy type is one of the most important types in the game due to the fact that Dragon Pokemon need to be countered, and Gardevoir takes advantage of this. Psychic/Fairy type combination is really good at the offensive side, and its stats, which are similar to Alakazam, are really good. Its Mega form gains the Pixilate ability, which gives it more STAB options. To sum up, Gardevoir is popular for many reasons other than its looks.
Number 6: Garchomp
Garchomp was always the most popular non-legendary Dragon Pokemon for a reason. 600 base stat total, Dragon/Ground type combination and a very wide movepool have made the Mach Pokemon a vey powerful threat that is difficult to counter. It also has a Mega Evolution, but it's somewhat a hindrance due to the Speed loss. But still, Garchomp is very popular and it will always be.
Number 5: Scizor
Scizor is almost everywhere in the game. Even teams with powerful legendaries will include this in the team. It is literally treated like a god for two reasons. The first is that it has access to False Swipe, which never faints the opposing Pokemon, thus becoming a good move for completing the Pokedex, and second, it has great offensive stats and typing, and a great ability to use. Also, by Mega evolving, it becomes a good combination of offense and defense.
Number 4: Scrafty
Scrafty is popular because it takes two very important types, Fighting and Dark, and combines them. Not only that, its defenses are really good, and it also has set-up moves like Bulk Up and Dragon Dance to boost its Attack stat. It is commonly seen in Elite Four teams, and sometimes in PvP teams. Even with a double weakess to Fairies, Scrafty has been a very popular Pokemon, and it will never stop being one.
Number 3: Weavile
Weavile is possibly the strongest non-legendary Ice Pokemon for many reasons. First, it has a great Attack stat. Second, it is very fast. Third, it has a great movepool, including moves like Swords Dance, Ice Shard, Icicle Crash, Brick Break, Low Kick and Night Slash. It is also very easy to find, as its basic form, Sneasel can be found in many places. The only thing that can stop it, however, is the 4x weakness to the Fighting type.
Number 2: Volcarona
Volcarona is one of the most popular Pokemon in the game, as it is the best non-legendary special sweeper. Access to Quiver Dance for easy set-ups, great STAB moves, like Bug Buzz and Flamethrower, and great recovery options like Giga Drain or Roost make this Pokemon impossible to knock out once it has started sweeping. Rock types like Tyranitar and Mega Diancie, which would normally counter it, would be defeated by Giga Drain almost instantly, meainlg that it has almost no counters. This has led to its banning from Rated battles.
Before I go to Number 1, here are some honorable mentions that did not make it to the list:
Lucario
Gallade
Tyranitar
Togekiss
Blissey
Breloom
Haxorus
Hydreigon
Salamence
Metagross
Azumarill
Kartana
And finally...
Number 1: Slaking
Slaking is literally the best non-legendary Pokemon. First, its hindering ability, Truant, is not, and will never be in the game. Second, it has the same base stat total with Groudon, Kyogre and Regigigas, which is 670. Third, its moveset is really good. It has Return, Double-Edge, Play Rough, Night Slash, the elemental punches and many more moves to use. It also has access to Power-up Punch, which increases the Attack stat every time it is used. Within a few turns, Slaking can become a deadly sweeper. Because of all of these reasons, it was obviously banned from Rated battles.
That was my list about the 10 best non legendary Pokemon in the game. Don't forget to comment.