What was the saddest?

[The Squatter of Amon Rûdh]

Since LMP has very eloquently gone over the scene between Sméagol and Sam on the edge of Mordor, I can only add the ending of Aragorn and Arwen's story. For me it combines the tragedies inherent in the fates of Men and Elves: for Men the tragedy is that they must at some time leave all behind them, but for Elves it is that any association with other races condemns them to bereavement.
The passing of Arwen is particularly poignant in that it gives such an impression of loss. Since she dies in Lothlorien we see her fading and that of the land together, which serves to remind one just how much is being lost; but the scene is also suffused with a feeling of inevitability that lends it a fatalistic air. This is the sadness of total despair.