The entire last four episodes of Wolf's Rain. My god, killing off all the characters we became attached to as the series progressed(TOBOEEEEEEEEEEEEEEEEEE ;____________; ) made me into a sobbing mess multiple times. I think the Earth revived and everyone resurrected though, so it's kind of a bittersweet ending. Just shows how good of a series Wolf's Rain is if it's that emotionally powerful.
I generally tolerate anime sadness pretty well...
but the animes that made me cry, or almost cry were
Spoiler for Clannad:
I had read the spoilers, but it still hit me hard. More so Ushio, though it hit me more later. Fuko didn't really bother me, I guess because it was so similar to Kanon, but I was sad at the end of the (clannad) arc where they explained the history of the dorm mothers cat
Spoiler for Noir:
When Chloe died. I think that was my first awakening to the fact that anime is not like American animation, and some times a main character will die a tragic death and not reappear in the next episode
I cried during lots of death scenes in anime, but the saddest one for me would be
Gotsumon and Pumpmon. I would've said Ushio, but she's revived in the end, unlike the truly dead unrevivable two. Didn't really feel much for Kamina or Maes Hughes (though his wife and daughter are saddening).
And Wizardmon's death, though also a permanent death, like those of the aforementioned pair, wasn't as sad as the deaths of those two Child Stage Digimon. It was tragic, sure, but it was dealt in such a way that it's a holy death rather than morbid (like the death of Christ, for example). Wizardmon's death caused Tailmon to evolve. Gotsumon and Pumpmon's deaths, however, achieved nothing beneficial.