I've watcher only limited number of anime. The saddest moments for me were when Ace died, when Going Merry burned down (One piece), Jiraiya's death and almost whole origin story of Nagato, culminating in Yahiko's death (Naruto)
I forgot about Steins;Gate, this scene absolutely hurt to watch. Of course it's not the first time you see Mayuri die, however, it is incredibly heart breaking, Okabe is backed into a wall knowing there is no way to save her without going to the other time line where Kurisu dies.
Couple that with this music, and you got bitch tears.
I wouldn't quite said its sad but the bleach opening 13 gave you that its coming to a end feel with the flash backs and all.
Spoiler About the bleach manga There has been a few major sad moments in the final bleach story that is manga only and personally I do like how they ended the Anime because these sad moments people who are fans of the anime only should not see. Like the Death Of the Head Caption Yamamoto and his Lieutenant.
Me personally I think this is the best bleach opening.
"Bleach Opening 13 Melody of the wild dance"
"All Bleach Openings" To see the final one play it from the 20:30sec mark.
Nothing will top Clannad After Story
Tomoya apologizing to Ushio
A new year, 10-15kg left to get rid off.
" #beach2015 "
Pretty much the whole Elfen Lied was sad
I haven't watched a lot of Anime yet and can't remember too many scenes specifically that made me tear up(or at least came close to tearing up) but I'd say a few episodes of Clannad(it didn't tug too often most of the time but there were a few scenes), a few from FMA:B, Fairy Tail specifically the scene posted earlier as well as her appearance in Extalia and her return to Earthland and rejoining Mira and Elfman at her grave, and currently the episode from Black Jack involving Pinoco's background and how she came to be.
Tearjerkers for me is clannad afterstory and anohana, moments, well they are all around. Otherwise there are alot of animes but hard to remember every tears moments and tell about them without spoiling everthing.
The end of Code Geass, where the crowd hails the death of the evil emperor with rallying cries for his killer, drowning out Nunnally's hysterical weeping for her poor brother.
Watching Hellsing OVA 10 and realizing its actually over.