This is how I'd do it, from scratch: Have a list of genres that open up in a tree of subgenres. Double click the genre and you get all the games in every subgenre listed, click a subgenre and you... only get that (surprise). Oh, that's exactly what Chroelle said above.

I'd name them really badly, because I suck at naming, but just to give suggestions. If I missed some obvious genres/subgenres, sorry, I didn't do research, ok? Some games go in multiple genres, no problem.
Genre - subgenre (game example; not displayed, real life examples)
- subgenre (game example; just to understand my subgenres)
- Other; all genres could have this, for games that don't fit
Adventure - 3D (Grim Fandango)
- Interactive Fiction (Scott Adams Adventureland)
- Point n' Click (Monkey Island)
Arcade Classics (no subgenre; Pac Man, Commando...)
Beat 'em Up - Fighting (Street Fighter, Mortal Kombat)
- Side Scroller* (Double Dragon, Golden Axe)
*I don't distinguish between forced scrolling and push the screen scrolling, nor between moving sideways or in other directions.
Exclusives (no subgenre; Harald Hardtooth)
Fun* - Board Games (Othello, Chess)
- Card Games (Solitaire, Hearts)
*I know "Fun" sucks as a genre; bite me.
Platformers (no subgenre; Superfrog)
Puzzle - Arcade (Chip's Challenge, Tetris)
- Other (The Fool's Quest, 7th Guest)
RPG* - Action RPG (Diablo, Zelda)
- Traditional RPG (Betrayal at Krondor, Might and Magic)
*Possibly Console RPG as subgenre, but I think they can be lumped with the other two.
Racing - 2D (Powerdrive, Super Offroad)
- 3D (Trackmania)
Shoot 'em Up - 3D (Uhm... I might put FPS in here, if not their own genre)
- Side Scroller* (Defender, Zaxxon)
*I don't distinguish between forced scrolling and push the screen scrolling, nor between moving sideways or in other directions. I put Shooters that don't involve space ships in here as well, such as Commando or Alien Obliteration.
Simulation - Business (GameBiz, Transport Tycoon)
- Flight Sim (Flight Simulator, includes tanks, U-boats, etc.)
- God Sim (The Sims, Populous)
Sports - Manager (Championship Manager)
- Player (Sensible Soccer, World Games)
Strategy* - Real Time (Dune 2)
- Turn Based (Master of Magic, Warlords)
*I still haven't figured out what 4X is... but if it's obviously missing, it's obviously missing.