Alright, I just had quite the skirmish about a certain trainer obtaining a Shiny Suicune when he hasn't got a single badge and nothing but a few pokemon. So, how about this.
[** - Note, Title is, basically, any pokemon that has been on the front cover of a game and a Pokemon the same caliber as them. This does not include RBGY.
TRAINERS: BABY LEGENDARIES ONLY. Also, only after the 5th Gym. [Phione, Manaphy, Victini, Jirachi, Shaymin, etc.]
ROCKET ADMINS: SIDE LEGENDARIES and lower. With a valid reason/worked to get it. [Heatran, Latios, Cresselia, Deoxys, etc.]
GYM LEADERS: TRIO and lower. With a valid reason/worked to get it. [Regice, Articuno, Suicune, Azelf, etc.]
ELITE FOUR AND CHAMPION: TITLE and lower. Must be included in a backstory/work hard to get it. [Giratina, Kyurem, Regigigas, Meloletta, Rayquaza, Darkrai, etc.]
BIG LEGENDARIES: Only applicable when obtained in the active story. Requires an extensive amount of threading, as well as the required in-game items for them. [Complete list - Arceus, Mewtwo, Kyurem-B, Kyurem-W. Also, any complete duo/trio of legendaries.]