There are other characters in my story that are Pokemon trainers, too. Don't forget that Mario was one of the Super Smash Gym Leaders. Even though those days are done, these people still grow as trainers. They have obtained new Pokemon and continue to get stronger. I have a list of Pokemon owned by Peach, Daisy and Rayman's friends, Mario, Luigi and Yoshi. Here are the list of their Pokemon from in first 3 Generations:

Mario
Bellsprout  Marowak  Parasect  Sandshrew  Poliwhirl  Slowbro  Graveler  Muk Poison
Gligar  Sunkern  Pineco  Heracross  Swinub  Slugma  Granbull  Delibird 
Glalie  Walrein  Ludicolo  Shroomish  Swalot  Solrock  Castform  Surskit  Slakoth  Ninjask  Loudred  Pelipper

Luigi
Weepinbell  Rattata  Poliwag  Abra  Gastly  Tentacool  Drowzee  Grimer  Mr. Mime Psychic/Fairy
Misdreavus  Quagsire  Yanma  Elekid  Piloswine  Magcargo  Mareep  Slowking  Sudowoodo Rock
Shiftry  Vigoroth  Electrike  Feebas  Kecleon  Lunatone  Snorunt  Lombre  Duskull  Sableye  Corphish  Banette 

Yoshi
 Lickitung  Chansey  Kangaskhan  Exeggcute  Krabby  Cubone  Diglett  Growlithe  Slowpoke Water/Psychic
Magby  Smoochum  Pichu  Igglybuff  Cleffa  Togetic  Spinarak  Hoothoot  Quagsire Water/Ground
Wurmple  Nincada  Azurill  Swablu  Wingull  Aron  Wynaut  Lotad  Gulpin  Spoink  Trapinch  Bagon  Camerupt 

There will be more on this soon.