Journey, PS3, but not exactly while playing it. At the end of the journey, no pun intended, the credits would tell you what other players you played with - your companions. It was my first play through. I met another person very early on and we played together the entire time, sticking close, chirping sounds of encouragement, trying our best to gesture which way to go, creeping beneath the cruising behemoths, keeping each other warm during the climb up the iced mountains.
Well we finish, the credits roll, I take note of their name (even wrote it down) and went about the rest of my day - really cheered up by the game. I didn't turn on my PS3 for a few days. When I come back to it, ready for another session of Journey, I see I have a new friend invite - and it's that player! Cool, I accept.
She messages me sometime later, tells me her name, and explains that she's been depressed for a while due to an accident that left her unable to leave home for a while, and this was the first video game she had played since Pokemon as a kid, on her brand new PS3 - brought to her that day by a sibling. And that I made the experience really special for her. I teared up.
We're still PSN pals, have played a few games together here and there over the years, but she hardly ever logs on anymore. She got better, got back on with her life as it existed before her accident I suppose.