The only sad FF I played was Crisis Core. Since it's the only one where the story is actually good. SE really sucks at juggling character development across multiple characters. When they focus on a few, they do a good job. Just because everyone knew how it was gonna end up didn't mean much. It's one of the few games where "spoilers don't spoil anything." Knowing just made it sadder because Zack was trying so hard and you KNEW it was all for nothing.
The saddest actual videogame i've ever played was Valkyria Chronicles, easily. That game is the first to ever make me cry. I've shed a tear before, i've felt sad before, but i've NEVER cried for a game. But that game just beat the shit out of me. Favorite game ever.
As for visual novels (technically videogames):
Clannad. An obvious choice. Probably one of the saddest visual novels i've played, and yet it was still hilarious too. It just knew when and how to get serious.
Wanko To Kurasou. I am not ashamed at all to have played this game. The ending of the better route (there's only 2) is RIDICULOUSLY sad. It's so cruel and mean (and yet it still has a happy ending >_>;

. It was really well done though.
Family Project. Dear god. That game has some sad moments. It's also ridiculously suspenseful near the end. Probably my favorite visual novel of all time. Translation errors aside it was pretty solid and like Clannad, it was pretty hilarious...but knew when to get serious.
I could name more but i'm lazy and about to play through Planetarian ~Chiisana Hoshi no Yume~.
EDIT: Holy shit almost forgot A Drug That Makes You Dream.
A bit too much hentai, but Aeka's route is really sad. I shed a man tear for that poor girl.