those poems..
Some of them are shatteringly beautiful, while others are merely lovely. If you don't know where to start, try "Harthad: a poem in two parts." If you want to have your heart broken, that is, in the Tolkien way. (Others I found very excellent were "An Extra Ordinary Life," "Frodo of the Shire," "Another Sunless Dawn," "The Plea of the Evenstar," "Only the Golden Dark," (Sauron's pov, of all things! It works), "Where you are Bound," and "They Say").
Note: Now I understand more of why Tolkien distanced the narrative more and more from Frodo's inner thoughts as he neared Mt. Doom (even though it breaks my heart to lose his voice) and in a way I'm glad he did. It's terrible enough from Sam's perspective, who can only guess at what Frodo's going through. The poems from Frodo's pov in Gorgoroth and Mt. Doom are really well done, but I couldn't bring myself to recommend them; you can easily find them on the site if you wish.
Note 2: Some are dazzling, some are merely quite good, and there are a very few based on THAT scene, which I would have avoided if I had known, and you may wish to avoid likewise; they are entitled: " A Kindly Friend," "Another Kindly Friend," and "Do You?". Many others are very dark, but they're canon-dark. (And no, "Go Home, Sam" is not based on THAT scene. I think it refers to an earlier attempt of Frodo's to leave Sam behind).