One of my favourite game endings was Shenmue 2. Well, okay, it had the start of a new chapter, but it took place in a completely different location; I still remember how it was to walk down those pathways with flowers either side. It also came with an opening-up of the narrative, beautiful hints of what was to come in the next game.
I finished Shenmue 2 recently and I am going to have to second this, it was just so peaceful walking through the mountains and forests, it felt very soothing. And it wasn't just a small scene, that was huge, it took me a whole afternoon to finish it. Sadly, I don't believe we'll see another Shenmue 3 in the future. Sigh.
And any Kojima game always delivers a good ending for me: Metal Gear Solid 1, 2, 3 and Snatcher. They were all good games by the way, not just the endings.
Mother 3 was also pretty emotional and deserves a mention here.
Metal Slug 2(?), I'm not sure which of the titles was it, but the one where in the end we ally ourselves with our enemies to destroy the alien invaders, and then that guy flies into the spaceship's main weapon to saves us all (just like in the Independence Day
movie). That was a great ending, it cracked me up.