I'm going to separate the game and the anime ones. Also, since I'll most likely end up seconding some of the ones mentioned here, I'll try to come up with ones not mentioned here instead. Not trying to be "special" about it. Just diversifying the tearjerkers here. ^^;;
Naturally, everything here are spoilers.
Anime:
1. Kuu's day of flight and the passing of the year festival (Haibane Renmei) - I liked Kuu the second I met him, so when she became the first character to leave, I took it pretty hard. (Not nearly as hard as Rakka, of course, but...) And after Rakka finally managed to overcome that, as well as her own sinbound status, Reki starts showing signs of having her day of flight approaching. (Which, due to her own sinbound...ness, isn't going to have a very positive outcome.) And then, the show proceeds to play out an absolutely BEAUTIFUL segment where the Haibane (sans Reki) go around passing out bell nuts to the people they care about. No spoken lines. Just footage and the music. I had to fight hard to maintain my male pride that time.
2. The departure of the Dew God (Natsume Yuujinchou) - I got this show as my Reverse Secret Santa project two years ago, and from the synopsis, I expected it to be something along the lines of Bleach. And then, the first episode went ahead and shattered those perception by punching me in the gut. Hard. Things got even harder in the second episode, wherein the show featured the Dew God in question. He was a yokai that had bound himself to a shrine, and the diminishing amount of worshippers made him shrink until he finally faded away. Natsume himself wanted to become a worshipper himself to save him, but the Dew God was having none of that, choosing instead to go alongside the last person who worshipped him.
"Once you are loved and love in return, you can't ever forget."
3. Bruce's death (Galaxy Railways) - For most of the show, Bruce came across as the main character's angtagonist, but -- maybe predictably, due to this being a Leijiverse title -- he had his own reasons for being the way he was. Earning the nickname Toxic Bruce due to surviving a whole lot of partners, he eventually turned into a bit of a loner with little concern for his own life. But with the help of his comrades, he finally got past that.... only to be shot in the back by some lowlife rapist thugs and dying. At that point, I wasn't as much sad as very upset. The show gave him this huge sendoff, but refrained from giving me what I wanted to see the most; his murderers being brought in for justice.
I cried later, though, when season 2 turned out to be a huge load of horseshit -- a collossal letdown compared to season 1. ^^;;
4. Alice's melancholy (Aria the Animation) - An anime set on a fictive future where the human race has terraformed Mars, renaming it Planet Aqua (due to it ending up consisting of 90% water.) There, they rebuild the city of Venice, renaming it Neo-Venezia. And seeing as Aria is one of the nicest and most cheerful anime of all times, deaths aren't exactly in large supply here. But young Alice still managed to put a lump in my throat every now and then, and it started in episode 11 of Aria the Animation. Alice, who is lacking in social skills altogether but had finally made some friends.... came to the realisation, through a conversation with her... well, upperclasswomen, for the lack of a better word... that the three of them would eventually succeed in obtaining their goals, which would have the unfortunate side effect of giving them far, far less time to spend together. The plot in question ran in tandem with the main character, Akari, and a friend of hers who come from Manhome (aka Earth), the two exchanging mails on a regular basis, which tends to turn into the opening and closing monologue for each episode. And after Akari monologues her mail to Ai-chan at the end of said episode, we get a quiet, meek "Akari-chan, I... kind of want to see you now."
5. The deaths of Hansel and Gretel (Black Lagoon) - These two kids are anything but sweet -- they're assassins with a penchant for playing games with their victims (read: performing some pretty damn unsettling experiments on them) -- but their backstories are horrid as all hell. Having the unfortunate reality of being children in a country that simply didn't have the necessary means to give them anything even remotely resembling a decent life, the two are sold into not just slavery, but the porn industry. The SNUFF porn industry, where children were forced to fight each other to the death. (with inevitable results on Hansel and Gretel's part.) Eventually, the two are hired to take down Balalaika, which naturally doesn't go well. One of them set off towards the main target, but is taken down in quite a nasty fashion. The other tries to escape, renting the Lagoon's company boat to take... her... to safety. There, Rock actually manages to make "Gretel" defrost quite much, to the point where she sings "The World of Midnight" to him. Unfortunately, "she" is shot upon reaching the dock that were supposed to be her destination. And then, to the encore of "The World of Midnight", she dies.
Games:
1. When Millennia is absorbed into Valmar due to Sera, shortly followed by Mareg's death (Grandia 2) - This is one where I wasn't sad or crying. I was FURIOUS. Sera's continuous cackling had me promising myself then and there that I was going to play until I shoved Ryudo's sword down his throat. It was clear long before that point that the whole thing with Valmar clearly wasn't quite as black and white as first assumed, and not only through Millennia, but also the little girl who obtained Valmar's eye. At any rate, I fulfilled the promise I made myself. (And got a few nice surprises while I was at it.
2.
Caim and Angelus' end (Drakengard 2) - In game 2, we later learn that the sacrifice Caim and Angelus made in the first game was basically them being massively screwed over. One of the boss fights, and perhaps the one I've wanted to win the least
ever... is the fight against Angelus who had gone mad from the burden she had to carry and the pain that went with it. The throat-choking mercy of their end, particularly Angelus', at least had that "at least they won't have to suffer anymore" quality to it. And Caim, that bastard, walks into the flames consuming her... and turns around and SMILES!
3. Children working in the mines (Lunar 1 and 2) - This aspect was just about removed from the remake of the first game, but for those who played the original, you'd eventually find out where they took the people of Burg... including the children. And then, in the sequel, they did the same with Borgan's magical aptitude test. And while I can probably assume Taben got his in the end, I always thought Borgan got off WAY too easily. He broke apart families and forced kids to work until their hands bled while forbidding them to see their parents or siblings, and Miria just FORGAVE him. And while nobody died in EB... presumably... the graves in the mines in TSS clearly showed that people were being forced to work until they fell and died from exhaustion, which, given the kind of labor we're talking about, is far more likely to involve the kids. Another one of those who didn't necessarily make me cry, but it certainly made me kind of upset.
4. Lilly's farewell letter (Grandia) - When I started playing Grandia, I thought Justin was kind of a dumb kid. And you do in fact start off the game controlling him playing a kid's game with some punks before making him go home and take a tray to the nogging from his mother. But by the time he headed off for the docks to follow his dreams, I was getting quite fond of the little rascal. What follows is maybe one of the best mother and son portrayals I've seen in a videogame; Justin is given a letter that he's supposed to hand over to the acting chief of an adventurer's club. Justin, who still has a couple of minutes, can't resist reading the letter. And this is where the game deserves the credit for being one of my favorite JRPGs simply for actually succeeding to make this scene poignant despite its laughably bad voice acting. The letter from Lilly is basically a heartfelt request for said acting chief to let her son follow his dreams... followed by a short chastising ending to Justin because she knew he wouldn't be able to keep from reading it. I think it just goes to show that scenes featuring partings can and will influence me just as much as character deaths, if not more so. It's hard to explain. I guess it's just the "I'll never see them again, but at least they'll be OK" factor.
5. ....well, seeing as you've taken all the other good ones I know, I'll just mark up Nei's death (from Phantasy Star 2) as my last entry. Sure, the game could do with a whole lot of fleshing out, but when all was said and done and I realized that she would never return to my party, her prescense was missed. And the unfinished manga I read based on Phantasy Star 2 certainly didn't help matters. Maybe it's just as well the creator never got around to doing the part where she dies. ^^;;