We've probably already had this thread, but a new one never hurts

. It's really hard for me to list a few of these, so I'll list my favorites for various genres.
Adventure: Leisure Suit Larry 1 and 2(PC), Myst (PC), Super Mario 64 (N64), Zelda: Orcarina of Time (N64)
Art: Color a Dinosaur (NES)
Fighting
[ul][li]2D: King of Fighters '98 (Neo Geo), Last Blade 1 and 2 (Neo Geo), SNK vs Capcom: Match of the Millenium (NGPC), Street Fighter II series[/li][li]3D: Fighters Megamix (Saturn)[/li][/ul]
Light Gun: Gumshoe (NES), Missile Defense 3-D (SMS), Terminator 2: Judgement Day (Genesis)
Pong: Pong (any version), Pong (Playstation), Windjammers (Neo Geo)
Platformers: Bonk's Revenge (TG16), Shadow Blasters (Genesis), Sonic the Hedgehog (Genesis), Super Mario Bros 1 - 3 (NES), Super Mario World (SNES), Quackshot (Genesis), many more.
Puzzle: Dr. Mario (NES), Money Idol Exchanger (Neo Geo), Puzzle Bobble (Neo Geo)
Racing: Mario Kart 64 (N64), Night Driver (Atari 2600), Virtua Racing (any version)
RPGs
[ul][li]Action (overhead): Secret of Mana (SNES), Ys Book I & II (TGCD), Ys IV: The Dawn of Ys (PCE)[/li][li]Action (platform): Blood Gear (PCE), Cadash (TG16), Ys III: Wanderers From Ys (TGCD preferably, though any version is good), Zelda II: The Adventures of Link (NES)[/li][li]First Person: Crossed Swords (Neo Geo), Double Dungeons (TG16), Shining in the Darkness (Genesis), Shining of the Holy Ark (Saturn)[/li][li]Turn-based: Cosmic Fantasy 2 (TGCD), Final Fantasy IV (SNES), Lunar (Sega CD)[/li][li]Sports: Dodge Danpei (PCE), Final Lap Twin (TG16)

[/li][li]Strategy: Dragon Force (Saturn), King's Bounty (Genesis), Shining Force (Genesis), Shining Force II (Genesis), Vantage Master Online (PC)[/li][/ul]
Shooters
[ul][li]Horizontal: Insector X (Genesis), Gate of Thunder (Duo)[/li][li]First Person: Chex's Quest (PC), Dark Forces II: Jedi Knight (PC, if that counts), DOOM (PC), Wolfenstein 3-D (PC)
[/li][li]Platform: Metal Slug (Neo Geo), Metal Slug 3 (Neo Geo)
[/li][li]Puzzle: Twinkle Star Sprites (Neo Geo)[/li][li]Vertical: Blazing Lazers (TG16), Demon Attack (Intellivision), Phelios (Genesis)[/li][/ul]
Space Exploration: Space Shuttle Project (NES), Star Control II (PC), Star Trek 25th Anniversary (NES)
Sports: Baseball (Intellivision), Baseball Stars 2 (Neo Geo), League Bowling (Neo Geo), NBA Jam: Tournament Edition (any port), Tennis (Atari 2600), Wii Sports (Wii)
Tagging: Tag (Odyssey)
Let me know of any big genres I am missing because it seems like I am missing a lot of important ones.