Perhaps the worst thing about the ending is how everyone calls you the Hero of Cyrodiil after the deed is done. Why is that so bad? Because you didn't do a damned thing. In the end, all you did was help Martin sacrifice himself.
It's easy to find the Dark Brotherhood (assassin) missions a little heartbreaking. Why? Well, when you arrive at the Sanctuary after your initiation killing, you are quickly introduced to a rather (disturbingly?) cheerful band of murderers, whom the mission-givers encourage you to talk to for advice on your "contracts". So after a while, you've gotten to know all of them, their quirks, even the mean old shopkeep, and the black humor surrounding the missions themselves is hilarious, ("If [soon-to-be-dead guy] doesn't quit that awful drug, it'll be the death of him!") and then you get to the halfway point. The guy who recruited you thinks there's a traitor amongst them, and in order to get the traitor, he orders you to kill everyone in the sanctuary. All of them. Even darling Antoinette-Marie. And you have to, if you want to complete the mission line. And you'd have to be completely soulless not to feel bad about it. I mean, the shopkeeper chooses now of all times to start being nice to you! Just to add insult to injury, it seems like the rumor mill chooses that moment to pick up all the rumors about all the new dead guys you had a hand in making. Jerks. It's enough to make you pull a Heel Face Turn...
And some other Dark Brotherhood targets are fairly likeable too. Matilde, "Next of Kin" or "Honour Thy Mother" are good candidates for those that go too far. They're among the worst things you're ever asked to do in any video game in a serious context.
The Arena battle for Grand Champion. Up till then, your predecessor, the Gray Prince, has been a jovial fellow, if a little worried about his past. When you find out that he's really the son of a vampire he goes straight into a Heroic BSOD, not even bothering to lift a finger to defend himself in the Grand Champion fight. The tear-jerking part? Everyone in Cyrodiil treats you like a hero for killing him... except his best friend, a Dark Elf in the Arena, who bitterly says, "Congratulations, Grand Champion. I hope it was worth it."
Even some minor details can provoke this. There's a cave in the Shivering Isles populated by elytra and gnarls. Toward the back, you will find a dead woman. She is holding a diary, which details her coming to the cave with her lover and him wishing to make the cave their home due to his finding other people stifling. She came to find the cave something of a prison since she could not leave without breaking his heart (and it having been populated by the aforementioned monsters). She planned to escape, but confronted him about it first, and he allowed her to leave. However, she broke her leg on the way out, and was unable to either leave or return, and he did not respond to her cries for help. Thus ends her story. Deeper in the cave, you come across the man himself - he is still alive but attacks you on sight. If you kill him, and read his journal, he details the same events from his perspective, including how heartbroken he was that she wanted to leave. His diary finished with him hearing her voice, but putting it down to the echoes of memory, not realising she is genuinely in mortal peril. There is no quest relating to these two; you will only encounter the story at all if you find and choose to explore this cave.
The entirety of the Shivering Isles tends to be depressing, if not Heartbreaking. To start, we have a realm that invites it's users in with a laughing Sean Connery like voice. Immediately after, it will either drive the "guest" insane, and spit him back out to be killed, or keep him/her there forever, thus cutting him off from his life. Next, for those that survive, there's the Gatekeepers death (which isn't so bad as far as these things go) but is compounded by the fact that you can use it's mother's tears to injure it further. The crying alone deserves a special mention, because that hints that the mother knows her child is going to die, and that she has seen it before, and she knows she's bound to making these things, just to see them die. Further in, we have an entire city divided into insanity, and the Dementia side is truly heart-wrenching. The people within are bound to a lifetime of sorrow and paranoia and the only way out (suicide) is punished by magical suicide cliffs that bind the souls of those who leap from them, only to be sentenced to stay there for all of eternity. To wrap this happy little party up, Sheogorath himself is depressing, as he is bound to continuously watch as his world is built up, and then see himself tear it down piece by piece, only to start again.
The fate of the Dwemer race. Yes, they were not the nicest guys in history and they did some dick things (like what they did with the Snow Elves for just one example among... quite a few). But even as creepy as the Dwemer ruins can be, there is a kind of wonder surrounding them. After all, these guys made steam engines, complex astronomical devices and effing robots. They had a scientific genius that the rest of the Elder Scrolls world could only guess at. But then they tried to make their own God, and... well, it all just went downhill from there. As unlikely as it may have been, and as ultimately destructive as it could have been... One can only wonder just how much better life might be for the denizens of Tamriel if the Dwarves could have used their technology to truly better themselves AND the world around them. Now all that is left of the greatest minds in Tamriel are rotting cities, rusting machines and one final member of their race, searching for his kin and ending his life diseased and mad.
Adding to this: In Skyrim, we learn that the Dwemer had managed to build a device that could read an Elder Scroll without the associated blindness. In other words, using science and technology, married to magic, they could see the future! And then their civilization vanished.