Mine can be grouped into sections of games that "feel" similar to each other:
GROUP 1 - My main choice
RPGs (consisting of):
- ARPG - Action RPGs - Loot collecting and monster smashing with story and character growth. Doesn't really belong in the RPG list - Diablo II, NoX, Dungeon Siege, Titan Quest, X-Men Legends, Baldur's Gate: Dark Alliance
- WRPG - "Western RPGs" OR "World Centric RPGs" - Gives the player a world and says go live in it, often giving the player control over creating his or her character. Often fast paced combat, although controllable (pausing, VATs) in some way - Oblivion, Skyrim, Baldur's Gate, Dragon Age Origins, KoTOR, Fallout 3, The Witcher, Demon's Souls, Dark Souls, Grand Theft Auto IV, Read Dead Redemption
- TRPG - "Tactical RPGs" - A blend of Turn based Strategy and RPG story/character growth - Final Fantasy Tactics, Disgaea, Fallout, Tactics Ogre, Jeanne D'Arc
- JRPG - "Japanese RPGs" OR "Character Centric RPGs" - Gives the player a character or party and weaves a story around them; mainly turn based, menu driven, slower paced then its Western counterpart - Final Fantasy IV, Final Fantasy VI, Final Fantasy XII, Dragon Warrior VIII, Suikoden
- MMORPGs 1 - I only put this section here as there are only 2 notable exceptions to the MMO genre that I like, more likely because they closely resemble the first 2 RPG sub-genres that I like than MMOs typically do - EVE Online, Guild Wars
GROUP 2 - More "Actiony"/"Story" games
Action/Adventure - Exploring, Shooting, Story & Platforming all in one - Uncharted, Tomb Raider, Cadash, Castlevania, Pitfall
Shmups - Shootin' and Powerups - R-Type, Heavy Unit, Raiden, Contra, Powerup Forever, Soldner X, Galaxian
Brawler - Beat up waves of enemies, often with combos, set in levels with a big boss at the end. - God of War, Devil May Cry, Final Fight, Double Dragon, Streets of Rage, Golden Axe, Nightmare Creatures
First-Person/Third-Person Shooters 1 - Exceptions to the rule, the few within this genre that I find good. - Armored Core, Twisted Metal, Resistance, Gears of War, and to a small extent Dead Space.
Platformers - Jumpin' and Shootin' with level design being as important as the enemies you are shooting. - Mario, Wonderboy, Mega Man, Portal
Stealth Action - Thief, Tenchu, Metal Gear Solid
GROUP 3 - Usually slower based "building"/"thinking" games
TBS - Strategy without the action, usually controlling a small squad or group - Heroes of Might and Magic,
RTS - Strategy and Action, often with micromanagement - Sins of a Solar Empire, Seven Kingdoms, Warlords Battlecry, Star Wars: Empire at War, Starcraft, Warcraft
Grand Strategy - Strategy that is over and above normal turn-based strategy, often involving more micromanagement of resources over combat - Galactic Civilization, Civilization,
Vehicle Simulation - controlling the vehicle is more akin to real life - Gran Turismo, Microsoft Flight Simulator
GROUP 4 - Games to play with multiple people
Music - Where you "play" the music - Rock Band, Guitar Hero
Fighters - 1 on 1 style beat up the computer or another player. - Soul Calibur, Street Fighter, Mortal Kombat, Primal Rage, Eternal Champions, Dead or Alive, Fatal Fury, Samurai Showdown
VS Combat - Competition against other people - Twisted Metal, Armored Core, Counterstrike
Driving - Racing cars down a track, beating the other racers - Rush, Need for Speed, Wipeout, RC ProAm
GROUP 5 - Games that are about building or creating something.
Construction - Build stuff - Minecraft
Adventure - Story driven "point-and-click" figure it out - Day of the Tentacle, L.A. Noire, Full Throttle, Heavy Rain
Puzzle - Simple "figure it out" games without the story - Tetris, Columns, Desktop Tower Defense
Simulation - Controlling something like real life - The Sims, Spore
GROUP 6 - The shit I generally never "choose" to play:
First-Person/Third Person Shooters 2 - Where it's all about shooting shit directly, often geared towards "team-play" and short "objectives" - Call of Duty, HALO, Battlefield, Counterstrike, Team Fortress, Left 4 Dead
Sports Simulation - Yes, there are a wide variety of sports, but most I don't enjoy - Hockey, Football, Baseball, Soccer, Tennis, Fishing, Golf, Pool etc.
Survival Horror - Survive while shitting bricks - Resident Evil, Silent Hill
MMORPGs 2 - Grind to the next level with other players - World of Warcraft, Age of Hyboria, Dark Age of Camelot, Final Fantasy XI, Rift
Rythm - Where you tap in time to the music - Elite Beat Agents, DDR
Party Games - Very casual, usually "wagglestick" variety games, no real depth, just designed to let everyone play around a TV - Mario Party, Super Smash Bros, Sly Cooper mini-games
Waggle Games - Less than useless games because of the disconnect of your actions to what actually happens on screen - The Shoot, Star Wars Kinect