With Proffesor Oak :
Bulbasaur,Kingler,Muk,Tauros (×30),Snorlax,Heracross,Bayleef,Quilava,Totodile,Noctowl (shiny),Donphan,Swellow,Sceptile,Corphish,Torkoal,Glalie,Staraptor,Torterra,
In Training :
Also there are the Unofficial and the Temporary ones.
These are the Pokemon that he didn't capture.But you don't want about those.
Note : Ash owned and the pre-evolutions of the fully evolved ones.Like Infernape and Torterra.(Exept Palpitoad,Snorlax,Raticate,Beedrill,Muk and Noctowl)