GameBoy Advance - Golden Sun - The colorful and detailed battles of this RPG classic on the GBA was more beautiful than anything else on the system at the time. The music was held back by the quite bad speaker on the system, but with headphones it kicked the butt with the handheld competition. 

Nintendo DS - Osu! Tatakae! Ouendan - Not for its presentation but for the unique gameplay that could not work without the touch screen. This for me was next gen controls. Still bugged out that the western version did not sell well. 

GameCube - Super Smash Bros Melee - Coming from the very blocky entry on the N64 this groundbreaking game looked fantastic, played fast and tight, made the GC-controller a staple and had so much content that the 10 fighters of the original felt cheep.

Dreamcast - Shenmue - Open and dynamic world, motion captured animations, randomly varying weather. Other later games did it better but there was simply nothing like it when Shenmue released.

Panzer Dragoon

At a time when 3D graphics were futuristic, the leap from Megadrive to this was insane.

Ridge Racer

Similarly, when 2D graphics were the norm, this was quite a showpiece.

Luigi's Mansion 

Nintendo's first foray into 6th gen graphics was a stunner in 2001, putting the Gamecube's hardware to good use with its impressive lighting and particles

Motorstorm

At a time when the PS3 was struggling to live up to expectations, Motorstorm was one of the only early games for the console that really showed off what it's troublesome hardware was really capable of. It still looks great to this day.