Moderated said:
I've already seen Elfen Lied, Angel Beats, Clannad, Clannad:Afterstory, and AnoHana.
AnoHana got the closest to making me cry, but didn't get the tears to fall. I mean, it makes me tear up just looking at clips of it or hearing the opening, but no tears fall. I want to find an anime where I can't hold back my tears.
Oh man. Oh man, oh man, oh man, oh man. Saikano is probably one of the greatest "tragic" anime's I've ever seen, and most people don't even know about it. I can't recommend it enough. It's basically about this huge world war that breaks out, and Japan gets involved. It's interesting though, because there's not much action, and we're given almost no details about the actual war. Instead it focuses on the impact war has on the population. One of the best war stories/romances I've seen in anime. It's a tad bit melodramatic towards the middle, but man, the ending really delivers. It reminded me a lot of Grave of the Fireflies and Elfen Lied, although it's nowhere near as violent. Watch it.
I have to recommend Berserk, assuming you haven't seen it. It's a medieval fantasy epic, and probably the best one ever written. I consider it my favorite anime/manga. It's a great tragedy as well, and reminds me a lot of the great Greek tragedies I had to read in school, like Oedipus Rex. Berserk is a very "traditional" tragedy in that sense. It's similar to Game of Thrones, but far better. If you watch one anime in your life, this is the one. It's pretty brutal, but if you can stand Elfen Lied then you can watch/read this. The Manga is far more violent, but I felt like the anime had better pacing.
I have to assume you've seen Neon Genesis, but since you didn't list it, I'll go ahead and mention it. The post modernist philosophy is terrible, but this show has some of the best character development I've ever seen in any anime. Period. The only anime that may surpass it in terms of character development is, maybe, the before mentioned Berserk. I still feel my chest seize up whenever I see the characters. It's a basic must watch for every anime fan, so if you haven't seen it, go and see it. And sooner rather than later.