The part after you piece together Rosetta and have to leave Ellie to die a horrible death by poison gas. Granted, she escapes on her own but some find it difficult to Press X to Not Die when prompted due to not wanting to leave her behind.
The ending. Isaac and Carver have crippled the Brethren Moon, momentarily weakening it, allowing the two to finish the machine and bring an end to the chaos that's been chasing after Isaac since the beginning of the franchise—but, immediately after they turn it back on. They are consumed in the storm as Moon is pulled into the planet to their inevitable death. And in Isaac's final moment as the two spiral down into the abyss created in the Moon's wake, he silently pulls out the photo of Ellie he carried unto—and it's pulled away from his fingers. And succumbs his apparent fate as the Brethren Moon collapses into the planet as it's torn apart by the machine. Although, it's heavily alluded and very likely that he and Carver may have survived with the ambiguous voice messageafter the credits. It doesn't make the scene any less tragic.
Earlier on Tau Volantis, the death of Buckell. It was to be expected since he was already injured, but it's still very sad to see such a good, kind man die. At least he didn't die alone.
The army killed everyone. No, really. They killed scientists and workers and then self terminated. The real kicker? The people who executed the order sincerely believed they were performing a heroic sacrifice to protect the rest of humanity. In the end, the massacre only made the catastrophe more likely to happen, making the entire thing a pointless tragedy.
There's a text log from the perspective of a soldier, after the Scenario Five order was given. He talks with the guy running the armory. They laugh and joke about their families and what they were going to do when they got home. Then the armory guy just lies down inside a body bag and shoots himself, and the soldier writing the log says he's looking forward to dying.
The fate of Tucker Edwards, the lazy asshole who panicked when SCAF were massacring everyone and locked himself away in a booby-trapped fortress. Not only does he eventually apologize to whomever is coming after him (specifically that it's nothing personal, but he's too scared to die), but the trail to him ends with his corpse and a suicide note stating he's too lonely to continue, before he apologizes to his dead colleagues for being an asshole and shoots himself. There's even a rather sad personal log in the crew quarters below him where he writes about his colleagues:
Personal log: Lt. Edwards LJG Chuck Sekowski: Hated country music. Bugged the shit out of me. A better man than I ever was. COR Valery Dietz: Too serious. Cute smile. Why didn't we ever hook up? I'm sorry I killed you. LCDA Sam Kettle: Workaholic asshole. The best of us. I wish we could have been friends.
Valery Dietz was on the verge of tears when she attempted to kill him. It's odd to hear some of such high rank to break down like that when they should be the ones setting the example. Perhaps she loved him back?
Finally finding (what's left of) Doctor Serrano shortly before the end of Chapter 18. You get to the last rappelling station and find a decomposed corpse next to a backpack and an audio log. Playing it allows you to listen to his final monologue, where he forlornly states that his knee is too broken to go on before going on to reminisce about his early years, and how his passion for xenotechnology was laughed at. The disappointment in his voice when he laments about how he'll never witness the Machine's reactivation is heartbreaking. It's especially poignant since, in a way, he's been by the player's side since the prologue - guiding both Tim and Isaac through the Machine's puzzles. And if it wasn't for his work on the Codex, Isaac would have never been able to defeat the Brother Moon.
A great deal of Carver's past (found primarily through his personal side-missions) can be really sad. It becomes easier to understand his guilt at several points, such as his third mission where it's revealed he seems to have had severe PTSD before Dead Space 3 from the things he has experienced as a soldier, he frequently lied and fought with his wife (including instigating a domestic violence incident that his son witnessed), and a recording reveals Carver nearly killed himself before his wife accidentally walked in on him. Hell, it's pretty unsurprising that the guy has some demons he needs to deal with.
In the DLC, the sheer fact that The Moons have honed in on Earth and are currently wiping out the human race is this. After all everything Isaac and every other protagonist of the series has done, the Necromorphs still won...
Making things worse were Isaac and Carver's last lines in the vanilla game; when Carver says that neither he nor Isaac would survive activating the machine, Isaac replies with "But Earth gets a tomorrow". They were willing to die to save Earth... and they failed.
The chapters first letter put together will spell R.I.P. This not only stands for the fate of earth, but might stand for the fate of the Dead Space franchise, considering EA basically got rid of Visceral.
Unless there's another game coming out, unlikely seeing as EA's given Visceral the boot, it's all over. Earth is gone, humanity is doomed. The universe will return to being dead space and there'll be a few hundred more Brethren Moons floating around, ready to eat the next civilization. All of Isaac and co's struggles throughout the franchise are utterly meaningless. You can't get much more of a Downer Ending than that.