[center]Thank You [@MissFortune] for this wonderful list :D
[hider=Uncapturable]Lugia and Shadow Lugia (Essential to Johto)
Ho-oh (Essential for the feeling of happiness)
Celebi (Time Travels)
Kyogre (Controls weather worldwide)
Groudon (Controls weather worldwide)
Rayquaza (Controls weather)
Jirachi (Awake 1 week every 1000 years and can grant wishes. OP but a fun story component, as each Trainer could make a wish before it goes back to sleep.)
Azelf, Mesprit and Uxie (Responsible for emotion worldwide)
Dialga, Palkia, and Giratina (Controls Time, Space and Matter)
Reshiram and Zekrom (Ying-Yang, Peace and War balance.)
Cresselia and Darkrai (Responsible for states of consciousness including Dreams and Nightmares)
Arceus (God of all Pokémon. OP.)
Xerneas, Yveltal and Zygarde (Essential for balancing Good and Evil and Order)[/hider]
[hider=Capturable]Zapdos: (None)
Articuno: (None)
Moltres: (None)
Mew: (None)
Mewtwo: (None)
Entei: (None)
Raikou: (None)
Suicune: @AbysmalDemon
Regice: (None)
Registeel: (None)
Regirock: (None)
Latias: (None)
Latios: (None)
Deoxys (NOTE: No alternate dimension travels please, keep things on this dimensional plane):
Manaphy: (None)
Phione: (None)
Heatran: (None)
Regigigas: (None)
Shaymin: (None)
Victini (NOTE: “victory Pokémon”, must be won.):
Cobalion: (None)
 Terrakion: (None)
 Virizion: (None)
Keledo: (None)
Meloetta: @MissFortune
Genesect: (None)
Diance: (None)
Hoopa (NOTE: No alternate dimension travels please, keep things on this dimensional plane): @1Charak2
Volcanion: (None)[/hider][/center]