Okay so in my opinion I think Angel Beats is one of the saddest anime of all time, however I will concede to Clannad because I've never actually seen it before, even though everyone says that I should.
One of the saddest scenes,and there are many, was the ending. And then your left thinking, "Wtf, what happened to my happy ending?! He was so close to touching her!"
HOWEVER, the most saddest scene was when Yui disappeared. She was always outgoing and loud and fun, always bugging the heck out of Hinata. But, in the end she finally got what she deserved: happiness. And the turn of events sent the anime into a spiral of even more sad scenes, including the ending.
BUT, none of the scenes would be possible without this really sad, yet amazing song! I absolutely love Ichiban no Takaramono.