Oh boy, if it happened like once...
My first cinema movie I was taken alone, without my siblings, of my choice, was Pokemon the First Movie, at wich I happened to get teary at the Ash supposed death moment. Great deal of time later I had a leak on FMA, when Hughes was murdered. At Kokoro Connect there was also this one touchy moment... and let's not forget SAO - Sachi death and the late gift. "twas first time in my life, that some humming made me cry.
Ugh, those ain't all, but certainly most memorable moments.