Lugia and Ho-Oh technically aren't Gamecube exclusive in the third generation, but to obtain them in a third-generation handheld game requires access to Navel Rock, which requires a Mysticticket for access, which in turn requires an event to obtain; FireRed/LeafGreen and Emerald can do this. For most intents and purposes, third-generation-origin Lugia and Ho-Oh typically originate in one of the Gamecube games (Lugia as the star shadow Pokémon of XD: Gale of Darkness, Ho-Oh as a bonus prize in Colosseum). A highly-popular Youtube LPer stands to be doing the task required for Ho-Oh in the near future (said LPer recently started the postgame in his Colosseum LP; yesterday's video had him losing the rematch against Skrub, meaning he's short half his on-hand cash from before that battle).
Two event Pokémon in the third generation also have Gamecube ties. Celebi can be obtained from the Japanese Colosseum bonus disc. Its American counterpart offers Jirachi. Jirachi can also be obtained from Pokémon Channel from the PAL region, which didn't get a bonus disc for Colosseum... --- I am a die hard Pokemon fan to the most, including the traditional hate of Yu-Gi-Oh.