The deaths of Thorin, Fíli, and Kíli, and particularly the Final Speech of the first:
"There is more in you of good than you know, child of the kindly West. Some courage, and some wisdom, blended in measure. If more of us valued food and cheer and song above hoarded gold, it would be a merrier world. But sad or merry, I must leave it now. Farewell."
Fíli and Kíli dying is understated in itself, but throughout the book the narration makes it clear that they're the youngest of the group, which, when you know about how Tolkien fought in World War I, makes the terrible waste of young men's lives all the more poignant.
Bert, Tom, and William being turned to stone. They were essentially just predators doing what predators were supposed to do. While they were an obstacle that needed to be overcome, it becomes Harsher in Hindsight when it's revealed in The Lord of the Rings that they did not turn back to normal at nightfall and were instead left as stone forever. Considering how affable they were doesn't help matters.
Since Bilbo left with no mention of telling everyone where he was going and hasn't returned for months, a year after his departure he arrives back to Back End to find he has been declared legally dead and his stuff is being auctioned off (indeed the better bits are already gone) and Otho and Lobelia Sackville-Baggins are ready to move in. What's more, getting the legally dead status revoked and the auction declared null and void proves such a hassle he has to resort to buying his own things back.
Bombur's enchanted stream incident is something that get worse and worse the more and more one thinks about it. He forgets the entire journey from Bilbo's house, which is tragic in a meta way since it's been such a journey, and then there's the fact that since he hasn't been able to eat, walk, or drink properly for nearly an entire week, he has no idea how he even got to be that way. And then, he who spoke his mind, but never about low rations, despite his weight. When he sits down and weeps about the food that ran out the day before -he w it comes off as sad and genuinely surprising for an otherwise hardy, snarky character. And while it's understandable that the other dwarves would be uninterested in hearing about Bombur's pleasant dreams, Thorin's response, which goes leaps and bounds ahead of just "Please do not talk about that"...
Thorin: You need not try, in fact if you can't talk about something else, you had better be silent. We are quite annoyed enough with you as it is. If you hadn't waked up, we should have left you to your idiotic dreams in the forest; you are no joke to carry even after weeks of short commons.
Watching the company turn on Bombur is pretty gutting, whether youd become taken with sassy, no-nonsense Bombur and then seeing him reduced to literally crying for help or whether you just plain expected better of the rest.
The saddest part was that Bombur was gripping the rope so hard that nobody could break it. Bombur never wanted to go under and while he was still lucid made every effort to avoid the enchantment's tantalizing allure. Even halfway asleep and Bombur was being as loyal as he knew how.
The animated movie
Although it's pretty short and limited (may or may not because of Limited Animation), Thorin's death scene is played as sad as possible, with Thorin apologizes and makes peace with Bilbo for calling him a coward before. Also, the Death by Adaptation for some other dwarves.
Bilbo: How many of our original company are left? Gandalf: Only seven. Bilbo: What about Thorin? Gandalf:Soon it will be six.
Specifically Bombur as well, who is given extra focus to show just what kind of awful, undiscriminating place the battlefield is. He is given extra focus and becomes Bilbo's friend throughout the travels. Like in the books, he is repeatedly shown as not a fighter, but still gets caught up in the company's 'war' manifesto. When we next see the poor guy, it's during the battle montage, where his bravado has shifted to utter confusion and terror, as all he can do is grasp his sword, frozen, before getting stabbed onscreen (without blood, but his agonized expression says it all.) And unlike Thorin's death, which the reader gets plenty of warning for (and a nice speech to help ease).
In fact, Peter Jackson decided that if Saruman couldn't come to Middle-Earth, Middle-Earth would come to him. Lee's work was shot on a sound stage and merged into the relevant scenes, so that he never had to leave the UK.
The music video for The Battle of the Five Armies' official song, "The Last Goodbye" sung by Billy Boyd, has scenes from both The Hobbit trilogy and The Lord of the Rings trilogy. It also includes behind the scenes footage showing Peter Jackson hugging the cast members from both trilogies after filming had wrapped. The song's content and video really hammers in the fact that The Battle of the Five Armies is truly the last Middle Earth film.
The Appendices of The Battle Of The Five Armies has a bonus video that pays tribute to cinematographer Andrew Lesnie, who died of a heart attack in April 2015. Philipa Boyens mentions that the first people who sent their condolences were the cast who'd worked with him over the years, saying that it shows how much of a family they were. The other person interviewed in the video was Christopher Lee, who said that he considered Andrew to be the greatest cinematographer he'd ever worked with (and considering how many films he'd been in, that's saying a lot). The tear jerker factor is raised even higher when you remember that this was only two months before Christopher himself sadly passed away, as well.