Resident Evil 4 (vital)
Pikmin (vital)
Harvest Moon - A wonderful life (vital)
Even though you have Pikmin2, it's still a shame to miss out on the original Pikmin - I'd say the original is more enjoyable, less complex, but has the same charm and gameplay. It's a lot less frustrating and still very challenging.
Harvest Moon always annoys me, the 2D visuals that seem to have stayed the same for decades, but this 3D rendition is bloomin awesome. It's got a great plot, while having a lot of freedom, it's just the best Nintendo RPG ever IMO.
Resident Evil 4. Not much I can say about it except that you should already have it. The Gamecube version has a style and atmosphere to it that was seemingly missed in other versions. It's a showcase of how great the Gamecube is - I've played other versions of RE4, and really nothing compares to the GC version.
I suggested 3 games, on top of Pikmin2 and Zelda etc, that's only 6 or 7 games total. But these games are unique, and should not be considered alongside other games. I mean take RE5 on the 360, more powerful machine, co-op... yet RE4 pee's all over it. I've never played a cutesy game on the 360 or PS3 that made me smile like Pikmin, or conjured up the same emotions as I experienced playing Harvest Moon. In all honesty, if I was only allowed 8 games and 1 console for the rest of my life, I'd go for a Gamecube and those games.