I'd say Eternal Darkness: it was one of those times where I bought the console to play a specific game, without knowing much more about the console itself. ED was even better than I expected and I enjoyed the Gamecube as a console maybe more than any other console I had after it.
Other than Eternal Darkness a lot of games come to mind but I'd like to mention:
- the first Viewtiful Joe: played to to death at every difficulty level, it was just too damn fun. Fantastic style, full of homages to tokusatsu, anime and games, really a gem.
- Chibi Robo: I lost count of how many times I replayed it, quirky and imaginative, very nice OST too. So much deep themes under the cutesy surface, really an underrated gem.
- Skies of Arcadia: I dare to say it could be my favourite jrpg but I still have to play some big ones. SoA may have cliched elements here and dare but it's the proof that you don't have to use outrageous elements to create a memorable mix. It's one of the few jrps that I replayed more than one time despite its length.
- Baten Kaitos: Bizarre game, really unique, it really took me by surprise. Like SoA, It's one of the few jrpg that I replayed more than one time. I still have to play the sequel, maybe I'll grab the remaster.
- The Two Lost Kingdoms games: Far from being perfect games, I loved their uniqueness. I got hooked on them especially because I played them after Baten Kaitos, that got me addicted to card-based systems. Again, maybe not the most refined of games but the From Software of the time already had the penchant fordoing something really unique.
- Custom Robo: Being a fan of mecha, especially super robots, I always was a fan of the CR franchise but sadly I wasn't able to play it on N64. CR for Gamecube was fun: not much of an rpg but really addicting action-wise.
- Gotcha Force: Loved it despite its flaws, it was a delight to get all the homages to mecha anime of the past and the OST was really nice despite some song being only instrumental. Especially one that was featured during the climatic battles and that had Hironobu Kageyama as a singer.
- Fire Emblem: Path of Radiance: My first Fire Emblem, the one that made me buy the other two games at the time for GBA. I was stunned by the fact you could lose characters permanently so I really tried to go with the perfect strategy to not lose anyone. It seemed a really difficult game at the time but, after playing the GBA one, I realized it was quite the easy appetizer. Really nice game, loved a lot of the subplots between the characters especially after using them a lot together during battles
- Mega Man X Command Mission: an odd one for sure. It's story really isn't the best, especially after the start but I found it being really addictive gameplay-wise, with sucha a great variety in attacks, forms and controls, tons of things to discover and to do and the addition of the GBA as a radar to find tokens. Nice cel shading too, some designs were really, really good. It can be seen a gimmicky annonyance but it added that extra flavor to an already nice experience.
- P.N 03 : Believe it or not, I absolutely loved the game. For sure it was an oxymoron of a game: a main character with fluid and ballet-like movements with tank-like controls. Yet I got instanlty hooked on it. Vanessa had a lot of charisma despite having few lines, the minimalistic style really appealed to me and I really got into the game mechanic and control and maneuvers like the quick 90° using the Z button together with the stick. It's one of those games that I replayed the most, even if just to beat a sequence of levels. And OST, so fitting!
- Killer 7: Absolutely bizarre yet unique, dripping with style. Maybe a bit more style over substance but it was a blast to play and especially to watch.
- Geist: The most flawed game of the list yet I'm still really fond of it. Unique atmosphere and some really great idea, sadly the realization of those ideas wasn't always the best. Still, I replayed it a lot: some sequences had a really eerie and gripping atmoshpere and the main gimmick of possession was really fun.
- FF: Crystal Chronicles & Four Swords Adventures: I put them on a single entry because we played them basically back to back and it was really a blast. Sure, it wasn't easy to gather 4 GBA but when we did we really enjoyed the cooperative game and the unique features that GBA connection provided.
I avoided other obviously great games like Paper Mario TTYD, The Metroid Prime games, The Resident Evil games, the Zelda Games, the Star Wars games and others, mentioning some of the games I played and replayed the most. Looking back at it, the GC really had quite the awesome library.