I started skipping the songs in LOTR as well. It wasn't until later that I learned a bit more about JRRT and his background in culture and linguistics study, and how he used LOTR largely as an experiment in creating and studying language. Next time I read LOTR, I specifically took the time to read through every line of each song, and tried to pay more attention to the different languages as well. I tried to think of the songs in terms of culture and how it evolves over time and tried to see how they functioned as they do in actual cultures. They help with the preservation of language, while simultaneously underscoring how it has changed. Summary: It was still tedious, but at least I had a better appreciation for their place in the books.
As for Melville, oh dear lord that was painful. An entire chapter on the left side of the whale, titled "The Left Side of the Whale". Then an entire chapter on the right side of the whale, titled "The Right Side of the Whale". Then a chapter on the flukes of the whale, titled "The Flukes of the Whale". And more. I don't know if I have the order or titles exactly correct, but those of you who have sufferred through Moby Dick on paper know that I am not exaggerating. My 10th grade American Literature teacher, who otherwise was a great guy and one of my favorite teachers (he's the one who turned me on to Tull, early Kansas, etc.) assigned this book, and I'm pretty sure no one actually read the whole thing. It just isn't possible for a 15-year-old mind to force itself to endure that kind of pain, not when Cliff's Notes are sold in the bookstore down the street.
Between that and Bartleby the Scrivener, I have great respect for what Melville tried to do, but little for the results.