A lot of the games mentioned here are very mainstream, quite popular titles. Zelda (Wind Waker or Twilight Princess), Tales, Skies of Arcadia, Eternal Darkness, Timesplitters, etc? Seriously, you think those are not that popular? Uh... they were popular. Quite popular. Stuff like Baten Kaitos and Fire Emblem were definitely successful as well, though Baten Kaitos Origins didn't do so well. I didn't like the first Baten Kaitos much at all, though, so I've never played the sequel. Fire Emblem's certainly fantastic though. I wouldn't call it unpopular though, it did well for its genre.
Anyway, what would I mention here? Hmm...
P.N.03 - GC exclusive, and a fantastic game! It's basically a shmup on feet, more than anything else. Consider it that and you might like it. It does seem to be love-or-hate, though. I liked it a lot.
Blowout - PS2/Xbox/GC 2.5d sidescrolling action/platform game. This launched very cheap -- I think it was $10 new -- and didn't get much publicity, but actually is a pretty good little game, well worth playing, if you like sidescrolling action/shooter games.
Donkey Kong: Jungle Beat - Nintendo's only sidescroller that generation, but yeah, it's a better game than most people give it credit for. Just be sure to play it with the bongos for the best experience. Note that the Wii version has some additional content, but isn't bongos-compatible, so I'd recommend the GC version over it.
Phantasy Star Online III: C.A.R.D. Revolution - This game definitely didn't get enough press, or success. This is actually a quite good card strategy game, and it's GC exclusive too. It's a good game, well worth playing.
Lost Kingdoms (1 and 2) - Two pretty solid card-battle action-RPGs. They were moderately successful, or at least the first one was, but aren't among the system's better-known titles, so I think they can make this list. I quite liked the first one, it's short but pretty fun. The second is good as well.
Spirits & Spells - This game's somewhat average, but it's a decent game, and it's definitely not something most people have heard of. Only released on the GC in the US, there's also a PS2 version in Europe. It's a railed-path 3d platformer. It's got some oldschool elements like one hit kills that send you back to the last checkpoint, so don't be fooled by how childish the box looks.
Zelda: Four Swords Adventures - The GC's two 3d Zelda games are of course quite popular (and very, very good), but this 2d one flew under the radar, and is one of the less successful Zelda titles. That's understandable, because that gen was probably 2d's low point in terms of success on consoles, and the game requires GBAs with GC-GBA link cables in order to play it in multiplayer (one player doesn't require one, only multiplayer, at least), but it's actually a very fun game. It IS best in multiplayer for sure, but it's a fun enough game in one player that I'd recommend it either way... though do try to get the stuff together to play it in multiplayer too.
1080 Avalanche - Somehow this game got somewhat overlooked at release. It did alright, I think, but SSX3 completely overshadowed it. I can see how that happened -- SSX3 was a very good game -- but this game's great fun as well. It is short, but a lot of fun while it lasts. I actually like this more than the N64 1080 game. A nice improvement for NST; their other GC racer, Wave Race: Blue Storm, wasn't quite as good as Wave Race 64.
XGRA: Extreme-G Racing Association (GC/Xbox/PS2) - This game, one of Acclaim's later titles before going out of business, is one of my favorite racing games ever. It got okay scores, and probably sold alright, but in part because Acclaim didn't last long at all after its release, and that it's the last game in its series, I'd certainly call it somewhat unknown now. As I said though, I think the game is absolutely amazing. I'm a huge futuristic racing game fan, and this is, in my opinion, one of the best ones. Everything about this game was designed to be fun. The game's basically the perfect Extreme-G experience, with some of the speed and style of XGIII, but gameplay that returns much more to XG 1 or 2, instead of being another Wipeout clone like XGIII was. I think that change was a very good decision, Wipeout's great but I didn't want XG to be Wipeout. Anyway, XGRA is just a fantastic game. It's got good music (though I always play in Dance only mode, not Rock or Mixed), good graphics, great speed, a good weapons system, great, varied track designs, and more.
I'm sure there are more.