A lot of Nintendo games, generally Zelda ones, have made me tear up during heartwarming moments and the like. Sometimes its out of sadness like in Majora's Mask.
Mother though.
Mother/EB Beginnings made me smile and tear up a bit during the ending. Earthbound made me feel conflicted and weird during the final boss. But Mother 3 absolutely destroyed me at many points of the story, but particularly the ending. It gets genuinely devastating... I don't like to only point out the sad parts though, the game has a fantastic story about dealing with loss and depression, and has many scenes that are lovely and encouraging.
Other M made me want to post angry stuff on the internet also. Praise Sakamoto-san.