Strongly seconding :
Arima -- His and Her Circumstances
Even if I found myself disliking his character at times
Minagi -- AIR
Minagi's arc has a special meaning to me due to real life experiences.
Misuzu -- AIR
Pretty much what was already said in the spoiler block above.
Rika and Hanyuu -- Higurashi Spoiler for Higurashi Kai (Season Two, unlicensed)
[spoiler]It is heavily implied that Rika may have experienced her friends being killed (often by eachother), and herself being murdered well in excess of one thousand times. She nearly gives up all hope of getting out of the repeating cycle of death. I'm adding Hanyuu to this because not only has she been with Rika through all of it, but she feels a sense of responsibility for the whole thing in the first place.[/spoiler]
Miyo -- Higurashi
I've never felt genuine compassion for a character I had formerly loathed until Miyo's arc.
Nina Tucker -- FMA
No explanation needed.
Hatori and Kana -- Fruits Basket
Chipping in:
My personal #1
The Okazaki Family -- Clannad After Story
[spoiler]I'm writing this as 'The Okazaki Family' largely to avoid spoiling the specifics as much as possible, but also because it's a pretty accurate assessment. If you're highlighting this because you've already seen Clannad After Story, you already know what I'm going to say. This is mostly for those who haven't seen it, but are curious why I'm rating them so highly...
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Tomoya's father, Naoyuki Okazaki, had to raise Tomoya on his own after Tomoya's mother died when Tomoya was still young. After the accident, Naoyuki turned to alcohol and smoking, and held frequent fights with his son. One day while arguing with his Tomoya on trivial things, he slammed Tomoya against the wall, dislocating Tomoya's right shoulder. Immediately after that, Tomoya refused to come out of his room, and by the time he finally went to the hospital, it was declared to be untreatable. The injury he suffered stops him from playing basketball ever again, which is his only passion.
Naoyuki distanced himself emotionally from Tomoya, and began treating Tomoya as a stranger but also sacrifices everything in his life just for Tomoya's sake, hoping Tomoya to grow up to be a proper man, unlike himself.
Tomoya ultimately becomes engaged to Nagisa Furukawa (later Nagisa Okazaki), herself having a rather tragic past. Though his father is in jail, and they are still not on good terms, he occasionally visits his father during the engagement -- mostly because Nagisa insists that he repair the broken relationship. As they prepare for the marriage, Tomoya starts to get his life on track, establishing for himself a proper job as an electrician and making the stable income necessary to support more than just himself. Some time after the wedding, Nagisa becomes pregnant with Ushio.
Nagisa wants to give birth at home, but her body is weak and frail, and Tomoya as well as her parents convince her that she should give birth at a hospital, due to the need for prompt medical attention that may be needed. Instead, Nagisa goes into labor during a winter snowstorm harsh enough that travel is deemed extremely unsafe in her condition. Though Nagisa lives long enough to see her child, she dies the same day.
Tomoya, unable to cope with the loss of his new wife, falls into cigarettes and alcohol -- much as his father did before him -- abandoning his newborn daughter to be raised by Nagisa's parents. Ushio is then raised by her grandparents for several years, never developing any special bond with her father. Tomoya has no attachment whatsoever to Ushio, as she looks much like Nagisa, and brings back painful memories for him. Nagisa's mother eventually engineers a plan to force Tomoya to go on a vacation with Ushio, and arranges for his paternal grandmother to run into him during the vacation.
After running into his grandmother, who explains to him the hardships that Naoyuki went through in raising him, Tomoya begins to begrudgingly respect his father more, but also realizes that what he has done to Ushio is exactly what his father did to himself. As he and his grandmother part ways, one of the most compelling emotional sequences in anime history plays out:
http://www.youtube.com/watch?v=kE38SKRT4ak
Afterward Tomoya begins his life anew, this time wanting to raise Ushio as a proper father. However, not long after he and Ushio begin to live together, the same illness that struck Nagisa with her frailty strikes Ushio, who succumbs to her illness during the cold winter, and dies at approximately age 6. Tomoya, upon seeing this, collapses into the snow himself. Some believe that he himself died of a broken heart.[/spoiler]
I'm not gonna write as much about the next two because I'd probably write two more blocks of text nearly as large as the previous one, so I'm just gonna throw the names out there:
Haruka Suzumiya -- Rumbling Hearts (Kimi ga Nozomu Eien)
Junior -- ROD TV