I usually only tear up instead of flat out bawl, but a few games have done this.
I haven't played most of those games, and frankly I am now very scared to, but the only game I truly shed tears for was the ending of Paper Mario: The Thousand Year Door. When the entirety of the world's inhabitants all came together and started rooting for Mario... It just hit me, OK?
This is one, and Okami is the exact same way as well for me, during the final boss fight. Ammy goes through something similar and the combo of the beautiful music and the world's inhabitants being all like 'We believe in you!' always makes me tear up. I think that type of ending is my weakness. xD
Pokemon Mystery Dungeon got me too, in Red Rescue Team, but it was when the MC/partner were ran out of as fugitives, and their friends greeted them before they left. I dunno, them seeing me off and promising to meet me again must've struck a heartstring or something as a kid!
Fire Emblem Awakening's chapters 9 and 10 left me sad and teary. In 9 There's a decision you have to make, I was so shocked that I let my ds sit for a half hour so I could think on it(
I later found it didn't even matter lol). The chapter after as a whole was so sad and depressing that I wanted to cry to it. ;-;