Shaymin
Pt: Gracidea obtainable in Floaroma Town Pokemon Center
HGSS: Gracidea obtainable in Goldenrod City Flower Shop
BW: Gracidea obtainable in Lacunosa Town Pokemon Center
B2W2: Gracidea obtainable in Striaton City Pokemon Center
Regigigas
Pt: Makes Rock Peak, Iceberg, and Iron Ruins available
Shiny Pichu
HGSS: Activates an encounter with Spiky-eared Pichu in Ilex Forest
Arceus
HGSS: Allows player to teleport from the Ruins of Alph to the Sinjoh Ruins
Celebi
HGSS: Initiates a battle with Giovanni at Tohjo Falls
BW: Allows player to obtain Zorua in Castelia City
Shiny Entei/Raikou/Suicune
BW: Initiates a battle with Zoroark in Lostlorn Forest
Events triggered by specific fateful encounter Pokémon (Bulbapedia)