A few others that I meant to mention:
Dancing Sword (GBA) ~ Beat-em-up where the combos have to be performed to a rythym.
Higemaru (Arcade, FC, MSX) ~ Pirate themed arcade-style games by Capcom. All kinds of awesome.
Shanghai Mini (NGPC) ~ My favorite Shanghai game. It would be impossible to dicuss every Shanghai variant ever, so this would be as good a place to start as any.
Windjammers (Arcade) ~ Surprisingly decent frisbee game.
Dokidoki Majo Shinpan! (DS) ~ The most ridiculously awesome crap ever. Playmore should be ashamed of themselves.
Otocky (FDS) ~ Kind of like Rez if it were for FDS.
Moon Lander (no idea exactly) ~ Classic that would be best discussed in a documentary-style sort of way.
Also, I'd appreciate if everyone could include the systems that these games are on so people know what they are getting into and so I can keep it organized without having to do research.
Here are a few of the platforms for the games that I suggested. Ill delete this part (to keep things less crowded) after you paste this into the OP.
Densha de GO! (Arcade, PS, PS2, others)
Jet de GO! (PS, PS2, PSP)
RC de GO! (Arcade, PS)
Power Shovel (Arcade, PS)
Tokyo Bus Guide (Arcade, PS2, DC)
Excitebike (NES, Arcade, FDS)
Clock Tower (SFC, PS, PS2)
Firemen (SFC, Saturn)
Toilet Kids (TG-16)
Capcom & SNK Cross-Over Fighters (NGPC, Arcade, others)
bit Generations (GBA)
NAM-1975 (Arcade)
Cabal (Arcade)
Fatal Frame (PS2, XBOX)
Silent Hill (PS, PS2, others)
Space Invaders (Arcade, MANY others)
Galaga (Arcade, MANY others)
Qix (Arcade, MANY others)
Fire Pro (SFC, PS2, several others)
Nintendo Wars (Advance Wars) (most Nintendo consoles)
Tecmo Bowl (Arcade, NES, SNES, Genesis, GB, PS, PS3, Wii)
Capcom's Marvel Themed Fighters (Arcade, others)
Little Wing Gameography (PC, Mac)
Puzzle Bobble (Arcade, SNES, others)
Bubble Bobble (Arcade, others)
Stand Alone Taito Puzzle Games (Arcade, others)
Stand Alone Konami Beat-em-ups (Arcade, NES, SNES)
Konami TMNT Games (Arcade, NES, others)
Konami's Other Shooters (Arcade, NES, SNES, MSX, & ports?)
Any Konami run 'n' gun that isn't Contra (Arcade, & ports)
B.B. Gun (SFC)
Rayforce (Arcade, & ports)
Taito Shooters (Arcade, & ports?)
Kirby (most Nintendo consoles)
Ninja Gaiden (Arcade, GB, NES, SNES, XBOX)
Mother (FC, SNES, GBA)
Mini Putt (C64, GB, FC)
Tempest (Arcade, & ports)
Missile Command (Arcade, & ports?)
Libble Rabble (Arcade, SFC)
Electric Yo-Yo (Arcade)
Legend of Stafi (GBA)
Puzzle-Dama (Arcade, SFC, others)
Gourmet Sentai Bara Yarou (SFC)
Shonen Ninja Sasuke (SFC)
Kung Fu (Arcade, NES, FC)
Godzilla games (multiple)
Nosferatu (SNES)
Super Sidekicks, or SNK Soccer Games (Arcade, NGPC)
SNK Baseball Games (NES, Arcade, NGPC, & ports)
Defender (Arcade, & ports)
Tomato Adventure (GBA)
Domo-Kun no Fushigi Terebi (GBA)
Karate Kid Games (C64, NES)
Battletoads (NES, GB, SNES, Arcade, & ports)
Raiden (Arcade, others)
Big Bang Pro Wrestling (NGPC)
Real Sound: Kaze no Regret (Saturn, Dreamcast)
Q*Bert (Arcade, SNES, & ports)
Motos (Arcade)
Gauntlet (Arcade, others)
Faselei! & Dive Alert (NGPC)
Melon-chan's Growth Diary (NGPC)
Mizuki Shigeru no Youkai Shashinkan (NGPC)
Kenta Cho Gameography (PC, & Mac?)
Ogre Battle (SFC, PS, NGPC, N64, GBA)
Party Mail (NGPC)
Delta Warp (NGPC)
Cool Cool (NGPC, DC)
Hanjuku Eiyuu (FC, SFC, PS2, DS, ports?)
Princess Tomato in the Salad Kingdom (NES)