For me it would be the following:
Homeworld 1, Homeworld:Cataclysm
Infamous 1 & 2
For the Homeworld games, they were one of the few times that I ever genuinely remember giving a shit about what was happening in the storyline. Other games had been ok at it, but the way they had structured the narrative of Homeworld, plus that little novel that they disguised as an instruction manual all served to suck me hard core. Seeing the mothership on it's maiden voyage, with Adagio with Strings playing as it launches genuinely choked me up. I remember getting chills about it. This monumental achievement of this planet, dying, and the people know it. They unite their warring factions, to pool their resources, to make a ship, to hopefully find a new home for their people. Knowing it was a last ditch effort to escape their slowly dying world. And the scope of it, from a cultural point was wonderful to me. These people had reverse engineered intersteller travel. Something we consider scifi (mostly). They had it, this was their first ship. The galaxy had literally opened to them. Then when we return from our maiden test flight, to find our world destroyed, the entire northern pole on fire, and then you get a report that some unidentified ships are attacking the cryo trays, holding the last members of our entire species. I went from shock to genuine anger, and gleefully killed those ships to the last man.
Everything about their journey into the unknown was great. The music, the artwork, the stark vastness of the space you play in. All of it.
And then Cataclysm came along and did everything HW 1 did, but even better. From the villain, to the voice acting, to the story. All of it was just great. How Kith Somtaw grew from a disregarded mining kith, into the Beastslayers, and welcomed into the halls of the Great Kith, was just awesome. The storytelling of that series was just great. HW 2 dropped the ball, but holy fuck balls did HW 1 and Cata hit all of my "Yes Please" buttons about what I look for in a story.
Infamous 1 & 2 is more of the above. Great storytelling, awesome mechanics. I genuinely felt like a super hero in that city, and the little things they did to let the game world reflect your actions was just great. And again, the game made me actually give a shit about what was happening to the little pixel people. I remember clearly, one time a good samaritan flagged me down to heal a wounded person. I jump down to do that (playing good guy), and as the samaritan watched me heal the person, a random thug on a nearby rooftop takes a potshot at me. Unfortunately, he ended up missing me, and killing the samaritan. And I couldn't do anything to stop it, because I was in the healing animation, and couldn't interrupt it. I had to watch, helpless, as this guy just trying to help dies for his actions. And I was pissed. I chased that thug down and ate his soul (literally) for what he did. And I loved that the game was able to get that reaction out of me.