Jeez, so many Pokemon I can think of. Since you specified "caught", I won't go into which Pokemon of Ash's I wish had evolved...
I'll just list a few:
If my memory serves me correctly, after Butterfree and Primeape departed, and Muk was permanently Oak'd due to its stench, Ash only had five Pokemon on hand for a large portion of the Kanto series. Some candidates I wanted to utilise that spot:
I'm always a fan of aspects of the games being used in the anime series. One such aspect was the orphaned Cubone from RBY, that could've been a great character. Similarly, the Game Corner has never been touched upon in the games, and I was so proud when I saved up enough coins to buy one of my favourite Pokemon, Porygon. Obviously, we all know why Porygon hasn't appeared, but still, things could've been different. Also, there was a Dugtrio you could catch in Diglett's Cave that I always caught, I wanted Ash to catch one, though admittedly probably not the easiest Pokemon to have on the main cast. From a more personal point of view, when I played Blue in '98, a Sandshrew/ Sandslash was one of the stars of my team and I always wanted Ash to have one as well. I always wanted Ash to have a Clefairy, one like Isamu Akai's could've been great. The anime Jigglypuff could've been a great team member, as could a Poliwag/ Poliwhirl/ Poliwrath like Red's. Ash's Haunter, if actually "officially" caught, oozed personality and could've been a really good character.
On the topic of Red's Pokemon, whilst I always liked Pidgeotto/ Pidgeot, maybe an Aerodactyl could've been more interesting?
Also, Eevee and an Eeveelution, even if it didn't evolve until one of the later Eeveelutions had been released, could've been a good character.
When Baby Pokemon were introduced in Gen II, I wanted Ash to get one. Specifically, I wanted Ash to get a Smoochum that would eventually become a Jynx. I think it could've been made into quite a funny character. Sudowoodo was a big part of the Johto region, similarly to Snorlax, and I used to want Ash to have one.
I always thought Hitmontop would've suited Ash and could've entered in P1 Grand Prix's like Primeape. I really wanted Ash to get an Aipom, so I suppose I was appeased later on, but I feel Ash's actual Aipom was a bit disappointing as a character.
Right. For a start, I've always been a fan of Ash getting all three starters. That is just me and what I like. On top of this, I thought Torkoal and Corphish were absolutely rubbish and definitely my least favourite of all of Ash's Pokemon, so Torchic and Mudkip.
I wanted Ash to catch a Wurmple/ Silcoon/ Beautifly at the start to sorta mimic Butterfree, but May did and I can't really complain about it tbh. The anime Spoink character could've been a good addition.
Kecleon, Volbeat and Duskull were the first three Gen III Pokemon I ever saw, and I was tricked by a friend into believing they were the new starter Pokemon and that they'd scrapped the Grass/ Fire/ Water thing. I wanted Ash to get all three. Looking back, Kecleon and Duskull could've made good characters, but Volbeat though? No chance, that would've been rubbish. I didn't like Gardevoiir so I didn't want it to evolve, but Ralts on Ash's team was something I wanted.
Until Goomy/ Sliggoo/ Goodra, I've never actually wanted Ash to own a final stage pseudo-legendary, but I wanted him to own a Bagon. That could've been a great character.
Piplup, just based on my whole starter thing. I have nothing against Buizel though.
I like Cranidos and, provided it didn't evolve, I think that could've worked well for Ash. Riolu/ Lucario is going to be a popular choice and yeah, it could've worked. The problem is though, I think once Ash gets one and starts getting into the whole Aura thing, I don't think he'll be able to "Oak" it without risking epic fan backlash, meaning he is stuck with Pikachu and Lucario permanently and only has four spaces for other Pokemon.
I still think the anime Hippopotas should've been captured.
I really wanted Ash to get a Vanillite/ Vanillish/ Vanilluxe as it was my favourite Gen V Pokemon. Failing that, I'd have settled for a Cubchoo. Similarly, I really liked Litwick/ Lampent/ Chandelure and Solosis/ Duosion/ Reuniclus.
I've never, ever, ever agreed with characters owning legendary Pokemon (even in my games!), but I do think if Ash was ever going to own one, it should've been Meloetta.
That is about it for Gen V really. I liked the Pokemon that Ash actually caught to begin with, I just wish more had been done with them. That is about evolutions though, not captures, so I won't go into it!
Gen VI and beyond...
For similar reasons to Torchic, Mudkip and Piplup, I'm sure in the future I'll look back and wish Ash had Chespin and Fennekin. For similar reasons to Wurmple/ Silcoon/ Beautiful, I wanted Ash to own a Scatterburg/ Spewpa/ Beautifly, particularly that anime one that appeared.
I also really like Phantump, Bergmite, Honedge/ Doublade/ Aegislash and Tyrunt. I'd definitely not want Phantump, Bergmite or Tyrunt to evolve though.
I doesn't suit Ash at all, but Swirlix/ Slurpuff is ridiculously cute and I'd love one to be on the main cast. Much better than that awful Dedenne thing.
Having traveled through the Kanto (x2), Johto, Hoenn, Sinnoh, Unova and Kalos regions, plus the Orange & Decolore Islands, competing in six regional Pokémon League competitions, winning the Orange League, defeating the Kanto Battle Frontier, seeing/ meeting each of the rare and powerful Legendary/ Mythical Pokémon, some on numerous occasions, and continually fighting vigilantly against six villainous teams, Ash has apparently now decided to go to school.