Ooh. This is hard. I've noticed a theme here. I'll go along and this is my list.
Dragon Age: Origins
KOTOR 1 (The TWIST)
KOTOR 2 (Sequel that was actually almost as good as the predecessor)
Red Dead Redemption (The FEELS!)
BioShock Infinite (Absolutely mind--blam!- at the end. Loved it!)
Honorable Mentions: CoD: BO (Best CoD in terms of both Campaign and MP), Fallout 3, Baldurs Gate 2: Dark Alliance, Goldeneye 64, Shadows of Modor, Gears of War (Not Judgement that was trash), Assassins Creed 2 (3 was meh and Black Flag was just boring), Skyrim, Oblivion, God of War 1-3, and etc. There is soooo many games. I did not mention Destiny because well there is no campaign. Also did not mention Last of Us because I've yet to play it yet but my roommate has it.
English
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Shadow of Mordor was Game of the Year for it's Story
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This is my list. It's going to be different than others.
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i have no problem with yourlist, sorry if I took my comment offensive