I agree with your sentiments, that tragedy changes with age.
The saddest, but maybe not tragic, is Arwen and Elrond's farewell. Though it is not discussed in detail, it hurts.
True tragedy for me is that Gollum couldn't be saved.
Well speaking subjectively I think the Gollum situation had the biggest effect on me. Particularly when he has his moment of doubt outside the lair of Shelob. I think Tolkien captured that really well. The film didn't have the same impact. I think they leaned too harshly towards Gollum's bad side in the film, whereas you get a more balanced and nuanced impression from the book. I don't think many tears were shed in cinemas when Gollum was swallowed up by the lava.
I would agree that the film version was sort of, well, blah. Except, there was one shot of Gollum's face and the joy as he's falling to his doom. That made me sad. Self-destruction of any sort makes me sad, especially when the person/creature doesn't see what they are doing to themselves and possibly can't help it. I wonder if JRRT had any experience with that or, possibly through the war, knew people with that experience.
An interesting thought about self-destruction. It wasn't really obvious to me that what happened to Gollum was self-destruction - wasn't it rather an accident? Still tragic, I agree.
And self-destruction is indeed tragic. Two episodes of it that feel tragic are
- Maedhros taking a Silmaril with him into a fiery chasm (thus fulfilling the Oath; although everything related to the Oath of Feanor is tragic) ;
- Nienor casting herself over the brink of Cabed-en-Aras.
But the third most tragic thing (on my list) isn't about self-destruction. It is the story of love between Aegnor and Andreth.
On a larger scale the whole history of the Noldor in the First Age is tragic, to say the least. The way the greatest Elves fell so far. The rise of fall of the Beleriand kingdoms.
On a smaller scale who can compete with the curse of Hurin?