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Main Pokémon games
After coming in possession of the National Pokédex, head over to Canalave City and head into the southwestern house. This house will have a boy who is not capable of waking up, and if you talk to him he'll mutter the word "dark", likely refering to Darkrai. After talking with the boys' mother, the player should talk to the sailor outside (the kid's father), who'll ask you to head to Fullmoon Island, where Cresselia is. After facing her, she'll flee, though will leave behind the Lunar Wing. Head back to Canalave City with the item in hand and give it to the boy to wake him up. Cresselia will now be roaming Sinnoh.
Cresselia doesn't appear inside of a Poké Ball in the Wii game Super Smash Bros. Brawl, but is rather one of the three different Pokémon that appear (and inflict some sort of events on the stage) on the Spear Pillar stage of the game (Dialga and Palkia, two other Pokémon, also appear here, as do the three Legendary trio Pokémon. Dialgia and Palkia have a couple of effects on the stage, including a laser cutting across the screen vertically or horizontally and inflicting moderate damage, and causing parts of the stage to fall. Once she appears, she'll use Psycho Cut, attempting to hit the opponents. Cresselia also appears as a trophy.
A Lunar Pokémon. Cresselia appears on Fullmoon Island and, once discovered, flies around different areas of Sinnoh. Her signature move, Lunar Dance, causes Cresselia to die but recovers all the HP and cures the status conditions of the next Pokémon her Trainer sends out. Cresselia excels at recovery techniques and is unusual in that she appears only as a female.