Big Games I've never played: Any Call of Duty game. I prefer my FPS to be sci-fi. Mass Effect: No excuse for this one. I've just never played them. Gears of war: Found it incredibly boring and too dudebroish. Demon's Souls/Dark Souls/Bloodbourne Fire Emblem: I have an Ambassador Fire Emblem game but I haven't touched it. World of Warcraft/Destiny/any MMO: MMOs are not my thing. Dark Souls and related:
Big Games I couldn't get into: Any Sonic game past Sonic 2 KOTOR: I just didn't like the combat system Final Fantasy XII: The style, atmosphere, and combat were so different from other Final Fantasy games that I was turned me off. I don't mind different, I just didn't like this kind of different. Lumines: At first I liked it but it quickly grew boring for me. NInja Gaiden (Reboot): I found the story to not be interesting. I prefer the NES games. Harvest Moon: This game is jut terrible. Monster Hunter: I tried the 3DS demo and hated it. Dragon Warrior/Quest: I prefer Final Fantasy. Super Mario Land 2: 6 Golden Coins: I just don't like this game like everyone else does.
I'll add more as they come to me or if you add something I forgot.
Anything in blue was added after the original post because I either remembered or your post inspired me.