The end of Planetarian: The Reverie of a Little Planet had me blubbering harder than I had since my parents got divorced (although your mileage may vary over whether you'd even consider that a game- it's a "kinetic novel", kind of like a visual novel with the gameplay removed).
I think I may have gotten a little misty-eyed at the endings of Illusion of Gaia, Terranigma and Lufia II, although I may be misremembering.
I think there have been some others, but I can't really remember. Video games have to work a lot harder to bring me to tears than, say, anime because it's usually harder to get the mood across.