A game that made you sad
Video games are only just beginning to seriously approach emotions that lie outside of the standard, "positive" feelings associated with the medium. To have fun is a major reason for many to play games, and rarely will you hear someone claim they want to feel "negative" emotions while engaging in their interactive pursuits. Of the latter group, fear seems the most prominent in games; sadness is far more rare. It seems sadness only exists in games in very small doses, primarily to augment the effect of later, "positive" emotions.
So from those games that feature sad moments, I must choose. As a player who yearns for these different emotions to be elicited by games, and is aware of them when they do show up, I would think this would be easier to figure out, but I still fail to recall many games that do it at all (or perhaps just ones that do it well).
Not surprisingly, most of the examples I can think of deal with love and loss, and it seems the story with the greatest number of those moments is the incredible Final Fantasy X. From the revelation that Yuna’s journey is one of sacrifice, to the final separation from the ephemeral Tidus, who the player controls throughout the game, FFX is likely the closest thing to a "sad game" that I can think of, although it does evoke many feelings besides sadness. No wonder it’s my favorite in the series.
Day 4 = Final Fantasy X
Day 3 = Animal Crossing
Day 2 = Too Human
Day 1 = Braid