For me, it would have to be Assassin's Creed II. The plot was amazing; I was extremely into it. Part that made me feel most emotional would have to be the beginning, when Ezio's family members got executed. All AC games are great in-general, but II stands out to me the most. :p
Halo 3. Seeing what was meant to be the end of Master Chief's journey. Playing through the first two Halo's made the experience even more bittersweet. I think Halo has some of the most beautiful music out of any game I've ever played. Sometimes the soundtrack alone is enough to make me emotional.