Simply put, Ash Ketchum is a bad trainer. He is the main protagonist of the Pokémon anime for over two decades, has very little to show for it. He only recently won his first Pokémon League Championship Tournament and has only barely captured a very small percentage of the available Pokémon in the world. He also has this really unfortunate habit of releasing several of his Pokémon, and every time he travels to a new region, he just takes his Pikachu. Rather than taking his overpower Charizard or his swanky Sceptile, he just takes his tiny, unevolved Pikachu.
At least Pikachu has a good reason to not evolve. Pikachu is the mascot of the entire Pokémon franchise, which is one of the most profitable series in the entire world. It wouldn't be beneficial in a marketing sense to no longer have Pikachu in the anime. Besides, nobody wants Ash to travel with a Raichu over a cute and adorable Pikachu.
Nevertheless, that still doesn't explain why Ash refuses to evolve a good percentage of his other Pokémon. For example, he used Bulbasaur and Buizel way too many battles to not have them evolve into their stronger forms. It doesn't even make sense why he shouldn't evolve some over the others. Evolving a Pokémon doesn't change them into a completely different Pokémon, but rather makes them even more powerful. If Ash simply evolved these Pokémon, he may have been a more successful trainer.
10 Bulbasaur
Ash's Bulbasaur actually had the opportunity to evolve in episode 51 of the original Pokémon anime series. The episode was named Bulbasaur's Mysterious Garden, and it centers on the topic of Bulbasaur being prepared to evolve. Though Ash was originally excited to have Bulbasaur evolve, it turns out his Bulbasaur thought differently. Ultimately Bulbasaur doesn't evolve in that episode, and he never does.
It's a classic episode from the original series, with a good message. Bulbasaur remained a badass throughout Ash's time in Kanto and Johto, sticking with him the longest of his original Pokémon besides Pikachu. However, it set up a very bad precedent in which Ash would continue to follow all the way to the Alola Region.
9 Totodile
Ash's Totodile was a Pokémon that preferred to jump around in joy rather than follow directions. But when he did listen to Ash, it was an effective member of Ash's party during his travels in Johto. Here's the weird thing though; of the three starter Pokémon that Ash caught in Johto, Totodile was the only one that didn't evolve.
Both Ash's Chikorita and Cyndaquil evolved, which made Totodile the lame duck. Admittedly, Totodile's evolutions were pretty ugly. They were far less appealing than Chikorita's and Cyndaquil's evolved forms. Even then, it's still strange that Totodile was left out of the group.
8 Corphish
Ash's Corphish was one of the more aggressive and battle-ready Pokémon that Ash caught in Hoenn. He originally fished the crab-looking Pokémon out of the sea, before eventually capturing him when he was attacking from underneath the sand. He would quickly use Corphish in his battle against the Gym Leader Brawly, and he stayed a powerhouse for Ash's team in early Hoenn.
Given Corphish aggressive behavior, he felt destined to evolve into the dark/water-type Pokémon Crawdaunt. Alas, it wasn't meant to be.
7 Buizel
Buizel was actually captured by Ash's friend Dawn in the Diamond and Pearl seasons of the anime. However, when she realized that Buizel was more suited to battling, she traded him with Ash's Aipom. Due to his love for one-on-one combat, Buizel ended up becoming one of Ash's most skilled fighters.
Given how powerful he was as just a Buizel, it's honestly surprising Ash's Buizel never evolved into a Floatzel. Diamond and Pearl was actually one of the few seasons where Ash actually did fully evolved a majority of his new Pokémon, so it was strange that Buizel was left in the dust.
6 Gible
Garchomp is what fans call a Pseudo-legendary Pokémon, which is a term to describe a three-evolution chain Pokémon with the highest base stats in the games. These Pokémon are generally considered to be the most powerful non-legendaries that players can catch.
When Ash got a Gible, which was the pre-pre-evolved form of Garchomp, fans were expecting Ash to have a truly over-power Pokémon in his party. It also was very convenient timing since the Sinnoh Pokémon League championship was going to start, and a Garchomp would be really useful to have. Unfortunately, that did not happen, and Ash lost in a battle where he had his feeble Gible in his party.
5 Scraggy
Ash hatched Scraggy from an egg, and ever since hatching, Ash's Scraggy loved to headbutt everything. Once again, Scraggy was one of Ash's most physically fit Pokémon within his party that somehow never evolved. What's odd with Scraggy's case is that there was less of a reason for him not to evolve than the normal reason.
The assumption is that the anime makes Ash keep his Pokémon in their pre-evolved forms because pre-evolved Pokémon are generally cuter than fully evolved Pokémon. Cuter often sells better, so there is some behind-the-scenes reason for why certain Pokémon stay the same. However, Scraggy isn't cute as is. They might have as well evolved him into a Scrafty.
4 Oshawott
Oshawott was one of the Pokémon at Professor Juniper's lab, who was meant to be given away to a new trainer. But Oshawott grew so attached to Ash after their brief visit, Ash ended up keeping the little otter-looking Pokémon.
Oshawott was with Ash for most of his journey in Unova, yet it just never evolved. It was a vital member of Ash's team during the Black and White seasons, though he admittedly acted like a coward sometimes when he thought he couldn't win a fight. It's possible it was his own cowardness that prevented him from evolving.
3 Snivy
Snivy is actually one of Ash's few confirmed female Pokémon in his party. Because of her gender, Snivy was able to use moves like Attract. Ash felt that she has the potential to be a great Pokémon for his team, so he caught her when she was caught stealing food.
Snivy proved to be a very strong Pokémon for Ash to use during his travel in Unova, which makes a lack of evolution for her really disappointing. As is, she was a little uptight. It would be cool to see her become a snooty Serperior.
2 Pignite
Of all three starter Pokémon that Ash caught in the Black and White seasons, Ash's Tepig was the only one that actually evolved. Tepig was another fire-starter Pokémon in the anime that was abandoned by their original owner and had Ash take them in. Ash's Tepig would get payback towards his original master in a double battle, evolving into a Pignite and defeating his old master's Emboar.
Even though Ash did evolve Tepig, he didn't go full measure and have him then evolve into an Emboar. It's a shame because Ash's other fully evolved fire-type starters, like Charizard and Infernape, are some of his most powerful Pokémon.
1 Rowlet
Unlike nearly every other unevolved Pokémon in Ash's possession, there's actually an in-show reason for why Rowlet never evolved. Ash's Rowlet is a little bit of an air-head and accidentally swallowed an everstone, a special item that prevents Pokémon from evolving.
The interesting thing about Rowlet not evolving is the fact that Ash's Litten did fully evolved into an Incineroar. The anime writers were probably expecting Litten and its evolution chain to be more popular than it ended up being. Rowlet's evolution line turned out to be the true favorites of that generation. Talk about betting on the wrong horse, or cat in this case.