So...my local game shop, which I consider to follow in the same spirit of GOG (i.e., making old console games and consoles available to those of archaic taste) had a sale and I picked up a Gamecube, all the prerequisite peripherals, and a copy of Metroid Prime for twenty five bucks. I've already found the rare Legend of Zelda heritage collection (LOZ, LOZ2, LOZ:OOT, and LOZ:MM), Paper Mario, Pikmin, and Metroid Prime Echoes to go with it. Now I'm wondering...anyone else have any recommendations? This place can get me pretty much anything I want if I'm patient enough, I've just always been a fan of the PS2, Metroid, and Zelda (the latter two of which I first played on the GBA). I basically made this first shopping list by browsing IGN's top 25 Gamecube games and dredging up memories of playing Ocarina of Time for the N64 - I know very little about the Nintendo franchises other than this.
Oh, and Metroid Prime is possibly one of the absolute best first person shooter / atmospheric suspense / space marine games I've ever played. Umm...not that there are THAT many that fit in that category...
So anyway...I just wanted to share my excitement, but I suppose I can make this a question - are there any CONSOLE SPECIFIC Gamecube games that I just shouldn't pass up? Thanks in advance!

I still have my original Gamecube, as well as 2 spares, and over 100 cube games.
It is a great little system that is just so faithful to run, and run.
Here are a few titles that I have found very worthwhile for the GC:
Skies of Arcadia - Fun RPG
Baten Kaitos - Eternal Wings and the Lost Ocean - Good RPG
Baten Kaitos - Origins - Second (and last) in the GC series
Tales of Symphonia - Good RPG
Pokemon Collosseum - I bought this as a deal with a System package - RPG
Cubivor - Survival of the Fittest - Odd, and likely the weirdest CG game - RPG lite Everything in the game are cubes including the sun and moon.
Lost Kingdoms II - 3rd Person
Beyond Good and Evil - 3rd Person
Sphinx and the Cursed Mummy - Fun 3rd Person
Metal Gear Solid - The Twin Snakes - 3rd Person
Chibi-Robo - Odd and fun little game
Goblin Commander - RTS game for the GC
Burnout 2: Point of Impact - Fun wreckage game
Mario Party 4, 5, and 6 for the Cube
MarioCart Double Dash
Super Smash Bros Melee
Zelda - Twilight Princess
Those are few I could list more but that should get you on your way.
Do not forget you can buy the add-on reader to play GBA games on the Cube as well.
The Wavebird controller is wireless and works great, and uses little battery life.
Any questions just ask, I think I have most things for the cube and have played most cube games other than sports games.

Hmm...I have a nice stack of GBA cartridges - is the Gameboy Player thing worth twenty bucks? I mean, that's what they charge for the system itself at the local shop...
And thank you very much! I'm starting to see some common threads here - for instance, picking up Baten Kaitos tomorrow for $5 is one of my priorities :D

CUSTOM ROBO. Like, seriously the best party game and a good custom robot arena game. Trust me.
The Resident evil remakes are amazing.
Timesplitters 2

I liked the look of Zelda: Wind Waker... even today it looks good, like a living cartoon. It pulled that off better than Borderlands or some other cel-shaded games too, even if they came later. A PC version with AA and AF maxed out would look stunning I bet.
Other than that though, my PC fanboy genes prevent me from missing too much else about the Gamecube. Metroid Prime had good music.

Baten Kaitos is an amazing game.
Also, any of the Mario Party games is great if you want something to do when friends are around. (I recommend Mario Party 5) also Super Smash Bros. Melee.
If you like the Pokémon games at all get Pokémon Colosseum.
The Resident Evil remake is spectacular, as is Resident Evil 4.
Super Mario Sunshine is quite entertaining if you enjoy a good platformer.

I have...Pokemon Sapphire. I haven't figured out HOW yet, but I have managed to be...not good at it. I do like it though.

For $20 it all depends. If you have a GBA, or DS that you use presently then wait for a better price. If you do not it is nice to have GBA games much larger on the TV screen.
If you buy one make sure it comes with the disk you need to make the two units talk to one another.
Also, the Wavebird is such a nice controller I think it is worth picking up. I have 4 plus one still sealed in the package for when one breaks, but the fact is nothing has every broken with the system.
They also make a DDR Mario Pad (it can be fun if you want to sweat), and Bongo controllers for a few games. I have had four of those hooked up a many occasions and people always seem to have fun.
I also picked up 2 (1 sealed still) 12' cables that really extend where the cube can be placed. I have it on an end table so if I need to reset I do not have to get up to do so.
The Baten Kaitos game is fun, it is not fast paced at all, but still a good game. Do not expect great voice acting though.
It can be frustrating but I like Skies of Arcadia, I have other RPGs but some are even older and more basic, but I have still enjoyed them.

Well, most game have been already said now, but I'll reiterate some:
- The Legend of Zelda: The Wind Waker (amazing game!)
- F-Zero GX (best racing game, IMO)
- Super Smash Bros Melee (although I prefer Brawl (on the Wii), this one is still a must. LOTS of replay value here)
- Super Mario Sunshine (not as good as SM64, IMO, but still good)
- Mario Kart Double Dash (very fun game, specially with friends to play!)
- Final Fantasy Crystal Chronicles (great game, quite different from other FFs)
- Pokemon Colosseum (good if you like Pokemon games. Get Pokemon XD too)
- The Legenda of Zelda: Four Swords (only good with gameboy advances and cables though)
- Sonic Adventure 2 Battle
- Phantasy Star Online Ep. 3 (Gamecube exclusive, online is dead. But still great card game offline!)
- Animal Crossing (fun game and great, if you never played any of those. Plus, lots of NES games inside!)
Now onto the multiplataform games:
- Viewtiful Joe (although the PS2 version has an extra character, Dante)
- Phantasy Star Online ep 1 & 2 (although online is dead, offline is still great, IMO)
- Soul Calibur 2 (Link as an exclusive character!)
- Sonic Heroes (no slowdowns here, compared to the PS2 version)

Disappointed about the lack of any mention of the TimeSplitters games. Yes, I realise they were multiformat, but they were hands down my favourite series of console FPS.

For the love of God, get Killer 7

I still play my gamecube because its an awesome console and I'm kinda collecting for it.
Anyway heres my own list of recommendations, I'll try naming ones that others havent:
-Ikaruga
-Starfox Adventures
-Crazy Taxi (I mean you just have to right?)
-WarioWare Inc.
-Geist
-Alien Hominid (gutted this didnt come out on GC in europe but its a great game)
-Super Monkey Ball
-Mega Man Anniversary Collection (has Megaman 1-8)
-Scaler
-Gun

I have the third one Future Perfect which is arguably the best with the improvements to SP. There was a rumor Crytek were interested in reviving the franchise and I hope so, after all the ending credits to Future Perfect did say the Timesplitters would return.

Well, it'll make sense once Crysis 2 is out to get the UK team working on something, and what they were working on before they got bought out seems a good a project as any. Although I wonder how TimeSplitters' more exaggerated look will apply with the CryEngine's emphasis on realism. Then again, TF2 did a good job of that on Source.