There was no game that made me "cry like a baby" but there were some instances when I have shed a few tears.
One example is in Danganronpa 2, the execution scene of Gundham Tanaka. Most of them are just bizarre or more "creepy" than sad, but this one just took the cake, of him putting his four hamsters (Sorry, his four dark devas of destruction) away so they wouldn't get hurt as he's trampled by a bunch of beasts, then looks at his hamsters one more time with a smile and to top it off, angelic critters fly down to carry him to heaven with somber music. A few tears were shed that day. ---