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F-Zero GX - Arguably the greatest racing game ever made. The difficulty level is honed to perfection as you fight for every milisecond of time, every microscopic inch of space on the track in order to master the game. Unbelievable sense of speed and last second finishes create an adrenaline rush unlike any other.
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Pikmin 2 - The epitome of how to improve with a sequel. Every last aspect of this game changes what was a mediocre series into a ****ing brilliant, generation defining event. And with a great 2player mode and a challenge mode, the replay value is great as well. I still pop it in occasionally, if only to hear the soothing soundtrack.
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Fire Emblem: Path of Radiance - The classic strategy RPG series comes to the Gamecube in all its glory. I say 'glory' relating to its gameplay - although its graphics and presentation can use work, it has near unparalleled gameplay and can provide many many hours of enjoyment. Even if you're not a big fan of the genre, give it a shot.
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Paper Mario: Thousand Year Door - Containing what has to be one of the all time greatest game translations, here's a sweet, genuinely funny RPG which uses the Mario universe to provide all sorts of fanservice and in-jokes that will have anybody with a little bit of gaming experience under their belts in stitches. The gameplay also suppliments this with a simple, yet effective combat system which requires some participation to become the best. With an audience too!
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Metroid Prime - There are haters for the game, but as a series regardless of how well you think it fits Metroid it is a phenomenal title. Utilizing several innovations - from the visor to the unique way the game handles platforming in first person, this title is a real experience. The visual style is distinctive and pulled off extremely well considering the hardware - it's one of the best from this gen.
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Super Mario Sunshine - The ultimate vacation game. Mario's acrobatics are at an all time high here, and it results in one of the most purely fun gaming experiences from the past generation. There are some who complain about the variety, and I'd say it is a problem for some... but I found it to be extremely refreshing to see multiple angles on this beautiful island. The FLUDD-less segments that come in now and then are extremely gratifying and some of the best platforming of any 3D game made.
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The Legend of Zelda: Wind Waker - Recently I replayed Ocarina of Time and Majora's Mask back to back and then went on to WW. I was pretty down that I saved this for last as I always remembered those two games being much more enjoyable. Boy, nostalgia sure is a bite in the ass. Wind Waker is so much better then these games - a hundred times more fluid, it doesn't feel sluggish, graphics that don't rape your eyes, and controls improved in every conceivable part of the game. It falls back, of course, in dungeon design and amount of dungeons... but in the end, the sum of its part is a game that looks better, sounds better and controls better and that wins for me personally. It's also one of the most beautiful games ever made, with an artstyle so fully realized it could be considered a substantial leap for storytelling in videogames.
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The Legend of Zelda: Twilight Princess - The Gamecube edition, undebatably the superior version of the game and worthy of all the sales (even though Nintendo raped its chances), is really a joy from start to end. Siren song of OLD NINTENDO... and I pretty much can't say anything that hasn't already been said.