A Word in progress list of GameCube and Wii games that can be played with just an 8-way joystick and buttons. similar to the PS2 Games on an Arcade Cabinet. thread.

GameCube
SHMUP
Chaos Field
Hudson Selection Vol. 2: Star Soldier
Ikaruga
Radio Allergy (Radirgy Generic)
Shikigami No Shiro II


Fighting Games:
Bloody Roar: Primal Fury
Bloody Roar: Extreme
Capcom vs. SNK 2 EO
Dragon Ball Z: Budokai
Dragon Ball Z: Budokai 2
Dragon Ball Z: Sagas
Mortal Kombat: Deadly Alliance
Mortal Kombat: Deception
Naruto: Clash of Ninja
Naruto: Clash of Ninja 2
Naruto: Gekitou Ninja Taisen 3
Naruto: Gekitou Ninja Taisen 4
Soulcalibur II


Run & Gun / Platformer:
Alien Hominid
Hudson Selection Vol. 1: Cubic Lode Runner
Hudson Selection Vol. 3: PC Genjin
Hudson Selection Vol. 4: Takahashi-Meijin no Boukenjima
Mega Man Anniversary Collection
Mega Man Network Transmission
Mega Man X Collection
Viewtiful Joe
Viewtiful Joe 2


RPG / Strategy:

Mega Man X: Command Mission


Puzzle:
Bust-A-Move 3000
Nintendo Puzzle Collection
Pac-Man Vs.
Puyo Pop Fever

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Wii
SHMUP
Bit.Trip Fate (WiiWare)
BlastWorks: Build, Trade, Destroy
The Castle of Shikigami III / Shikigami No Shiro III
Data East Arcade Classics (Super Real Darwin)
Geometry Wars: Galaxies
Gradius Rebirth (WiiWare)
Illvelo Wii/Illmatic Envelope Wii
Kyotokei (WiiWare)
Ultimate Shooting Collection/Milestone Shooting Collection
Milestone Shooting Collection 2
The Monkey King: The Legend Begins/Shin Chuuka Taisen: Michael to Meimei no Bouken
Ocean Commander
Radirgy Noa/Rajirunogia Wii
Saint
Simple Wii Series Vol. 4: The DokoDemo Asoberu - The Shooting Action
SNK Arcade Classics Vol. 1 (Last Resort)
Space Invaders Get Even (WiiWare)
Star Soldier R (WiiWare)


Fighting Games:
Bakugan Battle Brawlers
Chaotic: Shadow Warriors
Dragon Ball: Revenge of King Piccolo
Dragon Ball Z: Budokai Tenkaichi 2
Dragon Ball Z: Budokai Tenkaichi 3
Guilty Gear XX: Accent Core
Guilty Gear XX: Accent Core Plus
King of Fighters Collection: The Orochi Saga
Mortal Kombat: Armageddon
Naruto: Clash of Ninja Revolution
Naruto Shippuden: Clash of Ninja Revolution 3
Samurai Shodown Anthology
Sendoku Basara / Devil Kings X
Tatsunoko vs Capcom: Ultimate All-Stars

Run & Gun / Platformer:
Oboro Muramasa Youtouden
Eternity’s Child

Arcade / Classics Compilations:
Namco Museum Remix
Namco Museum Megamix
SNK Arcade Classics Volume 1



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These lists are likely woefully incomplete so if you know of other games that are confirmed to work 100% without analog please post them up.

added the following Gamecube Games:
Bloody Roar: Extreme
Dragon Ball Z: Budokai
Dragon Ball Z: Sagas
Hudson Selection Vol. 1: Cubic Lode Runner
Hudson Selection Vol. 3: PC Genjin
Hudson Selection Vol. 4: Takahashi-Meijin no Boukenjima
Mega Man Anniversary Collection
Mega Man Network Transmission
Mega Man X: Command Mission
Naruto: Gekitou Ninja Taisen 3

I also removed Bloody Roar and Bloody Roar 3.

"Bloody Roar" was never released on GC nor was the base version of Bloody Roar 3.
Bloody Roar Primal Fury is an enhanced version of Bloody Roar 3 that was released on GC in the USA and Bloody Roar Extreme is a further enhanced version that was released in Japan.