Off the top of my head, these are the games that pulled at my heartstrings this gen. Some a lot more than others.
Red Dead Redemption
Telltale's The Walking Dead
Batman: Arkham City
Metal Gear Solid 4
COD: World At War
Its been a while (and I need to replay it again) but yeah, thanks for bringing up Infamous 2...Good Cole FTW
Journey is also an emotional game for me; I've played through many times and every time is different. One time I played with a new player and showed him just about everything I could and he followed unquestionably, until he got hit by those flying monsters near the end ( ); we finished fine, but I felt so bad for him...what an emotional playthough. And then there are all the other good playthroughs (had one guy draw a couple dozen hearts into the snow at the end lol), but that one stands out...
Believe it or not, Demon's Souls and Dark Souls. Nothing like the emotions you get from beating each level and boss, and finally platting those games...yeah, it may not be a storyline thing, but dang, they can get you worked up.
Borderlands 2. If you don't have that burning hatred of Jack after that one mission (spoiler, so I'm not saying it. But if you've played it you know which one...) and just want to put aside all the new side-quests and go straight to killing him, something is wrong with you...
I'm putting Okami (HD) up because I only played it a few months ago. I can't remember exactly what it was about that game (too much lol) but what an experience. I really need to find a copy of Okamiden...
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I'd say Red Dead Redemption. The ending is one of the best I've ever seen in a video game. The whole game is memorable but when John Marsten dies, that I did not see coming. I just cracked open and a beer and said " Good game " .. lol