Twice in Final Fantasy VII. The famous scene where a certain person leaves the party permanently, and again when the catbot sacrifices itself and tells you "even if another me comes along, never forget me, the original", or something along those lines. Cried like a baby during that :(
The endings to Final Fantasy XIII, and XIII-2 were really emotional too. The former because "aw, that's so admirable, I love this bittersweet moment", and the latter because "holywtfbbq that was unnecessarily depressing and unexpected".
True Fire Emblem runs can be sad too (as in, not bothering to reload when a person dies). "Please, I don't... Want it to end... This way... Ahhh."
Yggdra Union has its sad moments too, like when you have to kill a character who was recently your ally.
That's pretty much it. There'd be more, but it'd probably not be very interesting.
I kind of teared up during the ending - not because of the ending - but because that game is freaking beautiful (not literally - i.e. combat) and I enjoyed all twenty seven hours of it. For me it has survived the years more than other certain "masterpieces" and I'd definitely take it over the PS2 remake.