I owned pretty much all major first-party sequels for GameCube, and I can't stress enough how many hours my friends and I sunk into Double Dash, Melee, and even Sunshine.
But, for me personally, the GameCube game I come back to every year or two and re-play is Thousand Year Door. Hands down, one of the best turn-based JRPG's I've ever played. So much content, so many side quests, Pit of 100 Trials, secret boss, collecting all the recipes, etc. It's really quite an amazing game. The two Paper Mario games since have regressed, and been smaller games with less to do, culminating in Sticker Star.
TTYD is the ultimate, superb, perfect Paper Mario game. I recommend everyone play it through to the end, even if the first two chapters start a little slow. Trust me, it's worth it.
The Screamapillar is easily identified by its constant screaming—it even screams in its sleep. The Screamapillar is the favorite food of everything, is sexually attracted to fire, and needs constant reassurance or it will die.
