I found the ending to be a bit too overdramatical for my tastes, but even if you weren't able to keep it dry, there's still the very final scene where
Spoiler Tidus flies through space, past Braska and Auron, and low-fives Jecht. Kinda makes it feel like he's coming home.
They never should have retconned that in FFX-2.
Oh yeah, The Last of Us gives you a sledgehammer to the face right there, especially since you're completely not expecting it.
Suikoden V still makes me all melancholic when I hear its music. Beautiful game that was. Well, not beautiful in a graphics-sense
I don't cry over video games, but some powerful scenes:
The Walking Dead:
Spoiler Kenny's death. All the other characters who died were memorable too, but none were like Kenny. He'd been there with you from the very beginning, gone through even worse hardships than anyone in the group, and still he went on. Sacrificing himself to protect that useless idiot Ben was a suitable exit for him, but still... Kenny's death was even more powerful than Lee's (even though you saw both of them coming).
The Last Remnant:
Spoiler Emma's death. Even though her opponent was completely unbeatable (he even snatches her sword between two fingers at one point) and able to effortlessly hold her off, she still kept attacking, in a wonderfully choreographed scene until she was finally out of strength, and the Conqueror kills her without moving a single muscle in his face.
Recettear: An Item Shop's Tale. http://i.imgur.com/UeOQr.jpg.
Persona 3:
Spoiler The ending, of course. As the protagonist falls asleep in Aigis' lap, the meaning of the subtle dialogue option, "Close your eyes", only hits home after a few seconds. The fact that nobody even remembers all the trials they've gone through together is also crushingly sad, since they all just go back to being ignorant high school students interested in being popular and getting good grades.
And
Spoiler The http://www.youtube.com/watch?v=3femcV7WotI. Everyone chooses to forget the doom of the world approaching and live out their last month in blissful ignorance until the world is destroyed.
Persona 4:
Spoiler The http://www.youtube.com/watch?v=qCodLLVVVNQ. Almost impossible NOT to get except with a walkthrough, the bad ending is less dramatic than P3's, but still has terrible implications. The protagonist's niece dies and her uncle is left all alone. The entire group knows they've indicated the wrong man as guilty, leading to the innocent suspect's death, the mist still hangs over Inaba and will never lift, and the shadows will continue to murder. The credits music being the same as the True Ending's final dungeon makes it even more leaden.
What I liked very much about The Last of Us, by the way, apart from the entire game being awesome, was that temporary allies don't always follow you until they die horribly. With quite a few of the temporary group members, you just part ways when you reach your destination. It was very refreshing to see, since most games these days try to go for cheap drama by killing off allies, and The Last of Us, steered away from it often, making it far less predictable.