Screw individual games, I can lump the games I haven't played into entire genres.
-MMORPG-
A friend bought me World of Warcraft in hopes I would join him on raids. It came with a month free. I played maybe 20 hours, met up with the friend only once, and played until the free month was up. That was the first and last MMO I ever played.
-RTS-
Played about two stages of the original Command and Conquer back in the 90's, and that was about it. I can't think of a single RTS game I've ever played since.
-TRPG-
I tried several times to play Final Fantasy Tactics, but never made it past the intro stages. I logged several hours into FFT Advance, but the fun stopped once I kept losing on a stage that took 30 minutes. And that was it, I never picked up another TRPG again.
-Hack and Slash-
Oh I've tried several of these games (God of War, Metal Gear Rising, Devil May Cry...), but none of them I've played more than 30 minutes before being bored to tears. A common theme through this list is that I get bored with any game that's non-stop action.
-Third Person Shooter-
There is only one TPS that I ever played to completion, and that was the Mass Effect series. The combination of it's story and long segments of non-shooting was enough to allow me to enjoy my time with it. But I can't think of a single other TPS game I've even bothered trying.
-Online Games in General-
The typical rule-of-thumb is that if it's online, I probably haven't played it. Having said that, I've put a combined 100 hours into the Splatoon series. I also find myself playing Smash Bros and Mario Maker online sometimes (though I'd say that accounts for 3-5 hours at most). And if you want to count it, I used to participate in LAN parties playing Quake 2, Unreal Tournament and Worms. Beyond that, though, I can't think of any other game I've played online.
-Horror Games-
I played the first two Resident Evils, and even that was a miracle. I hate anything horror, both video games and other media.
And finally, here's a list of some big games I've never played from genres I do play:
- Call of Duty series
- Battlefield series
- Halo series (except the first one, but I've never beaten it)
- Forza series (except Horizon 4)
- Rock Band series
- Animal Crossing series
- Any Tomb Raider game that didn't release on the PSX
- Most games made by Bioware (exception is the aforementioned Mass Effect series)
- Games made by Platinum (except maybe 30-60 minutes of Metal Gear Rising)
- Games made by Blizzard (except my aforementioned time in WoW)
- Games made by Epic games (except the original Unreal Tournament)
- Damn near every Pokemon game (exceptions include Blue, Emerald, Stadium, Snap, and Go)
- And like Ian, Timesplitter series