Metroid Prime 1 had strong more consistent art direction than Metroid Prime 2.
That gives Metroid Prime the nod for me. Star Fox Adventures definitely is very pretty.

The Legend of Zelda: The Wind Waker is probably the one that has held up for me over time.
Fantastic art direction.

Rogue Leader

Long time lurker, haven’t logged in for years, had to for this one!

Resident Evil Remake for me! It’s very rare that realistic games graphics hold up, even more rare when the game is 3 generations old. Must be a combo of good art direction, fixed camera angles, and the pre rendered backgrounds. I think that this looks better than both 0 and 4 on gamecube.

Resident Evil (remake)
Resident Evil 0
Resident Evil 4
Soul Calibur 2
Metroid Prime
Metroid Prime 2
The Legend of Zelda: Twilight Princess
Final Fantasy: Crystal Chronicles

(and credits to Star Wars Rogue Squadron, Need for Speed Underground 2, Super Mario Sunshine's water, Starfox Adventure's water & fur effects, Baiten Kaitos 1 & 2, Metal Gear Solid: Twin Snakes, Prince of Persia series, Splinter Cell series' & Ghost Recon 2 & Gun).

Also games with a timeless art direction include - The Legend of Zelda: Wind Waker, Mario Kart Double Dash, Kirby Air Ride, Paper Mario: The Thousand Year Door, Legend of Zelda Four Swords Adventures, Warioware Mega Party Games Inc, Viewtiful Joe 1 & 2, Naruto Clash of Ninja (Resident Evil 0 & 1 also seem timeless too, due to clever pre-rendered & lighting techniques).

Special Credits to the cutscenes in Fire Emblem: Path of Radiance. They still look beautiful now.

The Rogue Squadron games looked like they could have been on the XBox 360.

Star Fox Adventures still looks good today.

Resident Evil Remake had perfect use of pre-rendered environments

The Metroid Prime games used an insane amount of polygons for that generation.

Cell-shaded games like Wind Wker and Viewtiful Joe are timeless.

Resident Evil Remake and The Wind Waker are my picks.

Technically, probably Rouge Squadron II/III - bump mapping and self-shadowing, now that was definitely not something to be seen much (if at all) on GC.

From pure visual standpoint, there are quite a few, all already mentioned in the thread.

Super Mario Sunshine.

The water especially is amazing.

Without a doubt Zelda Wind waker. I'm still impressed to this day and an easy example of how stylization and artstyle can enhance graphics more than realism. If we're talking realism, Twin Snakes maybe, it's hard to judge now but I spent most of my time being blown away on ps2.

Twilight Princess was on Gamecube. Wow.