Although it probably has more effect if you played Phantom Hourglass beforehand, finding Linebeck's grave in Spirit Tracks is pretty darn depressing. In a mixture of Heartwarming and Tear Jerker though, the message on the grave says "Here rests the legendary Captain Linebeck."
Also, Right before the final boss of Spirit Tracks, when Malladus kills Byrne.
The trailer for Spirit Tracks includes the scene where Link and Zelda hold hands; you'd expect this to be a happy moment in the game, right? Well, it wasn't (just) that they were holding hands because they liked each other. They were holding hands because the Lokomo, their best allies, and Byrne, the man who pulled a Heel-Face Turn and sacrificed himself to save their lives, had just ascended to a higher plane of existence. They had just been through the toughest, most exhilarating, craziest adventure in their lives, and they were the only ones who came out of it still alive. The clasping hands wasn't just a Ship Tease moment — it was an affirmation that all they had left was each other.
Disorientation Station. It's one of the many optional minigames/sidequests in Spirit Tracks. A guard from Hyrule Castle is all the way out at that little station in the middle of nowhere, and he tells you that he and his friend went to find the treasure in the maze. He backed out after encountering a giant fire-breathing plant, but his friend continued searching, and hasn't come back. He asks you to go in and find him. While navigating the maze, you may encounter a message from the lost guard:
To my eternal friend and treasure-hunting partner, I can't seem to find the way out. I believe I am hopelessly lost. I don't think I have much longer left, so I want to apologize to you. I had originally intended to claim the treasure for myself... Even though you always looked out for me. When you ran off, I thought nothing of it and went on to find the treasure. I was a fool. I want you to know that you shouldn't waste any worry on me. Just move on with your life and please, think of me every once in a while. You are, were, and will always be my dearest friend. Farewell.
And it only gets sadder when you leave the maze and tell the first guard about the message. It's a surprisingly tragic conversation for an NPC who bears no relevance to the main plot.