For the purposes of this rant, I'll count Legendaries and Mythicals as the same thing.
Ho-oh (as his last-ever Pokémon), for obvious reasons. Latias as well, it's one of the first legendaries that actually made sense for Ash to have, since it wasn't portrayed as this god-like being and had a great relationship with him. Giratina, as much as it would've made no sense for a kid to have a practical God in his arsenal, was another mon he had a good relationship with. Then there's Victini, who would've been incredibly broken with its ability to ensure 'victory', but was close enough with Ash that I wanted him to catch it anyway. Still, I at least understood Ash not getting some of them. After all, they were from the movies, which were always in their own weirdly uncomfortable part of canon.
Then, they introduced Meloetta and Nebby.
Okay, so why didn't Meloetta become an Ashmon at the end of its journey? These two had such a great relationship together, better than multiple members of Ash's actual BW squad. Then they made it worse a few years later, by making Nebby come SO close, but not committing because they...just didn't feel like it I guess? Or maybe it's because they just didn't want anyone catching a Pokémon of that caliber. Well, at least they stayed consistent and nobody will ever end up catching and owning a Pokémon of the same power level because that would be ridiculous.
Anyway, aside from these Pokémon who just have some sort of bond with Ash or are significant in some other way, I really wanted him to catch Suicune someday, since it's a Legendary he actually showed some interest in catching back when he was allowed to do that. Too bad the writers don't want anyone catching this obviously special and mystical Pokémon, so Ash is locked out of ever getting one, just like everyone else in this show. And if someone does catch it, I'm sure it'll be someone who's significantly linked with Suicune in some way, rather than it just being in there to fill some imaginary checklist or be a convenient capture to move the plot along.