Title has been edited. I didn't think of the ambiguity.
The only science fiction story about bad immortality I can think of off the top of my head is, "I have no mouth, and I must scream" by Harlan Ellison, but that is more to do with UFAI than anything else. I know the Dune mythos has some comments on immortality, but I've only read the first book.
Hmmm... Tolkien has some rather choice things to say about death in the Silmarillion IIRC. I believe the context is that he is speaking about the elves being envious that men can die rather than pass to the Halls of Mandos. In the downfall of Numenor, Tolkien speaks quite extensively about men rejecting death being an evil thing, and inheritance being screwed up because of it.
I would love more sci-fi/fantasy examples.
Edit: Tuck Everlasting! That book is centered around the theme of immortality, and perfectly 'conventional' in its treatment of immortality.
In the third part of Gulliver's Travels, there is a rare birth defect that causes people to live forever. They do not stop aging, though.
This may not be the right place for this, but I need quotes about death coming from the orthodox (normative, non-LW) position on death. I'm working on a project that will eventually be at least tangentially LW relevant, and I want to have some good 'pro-death' quotes that I can adapt for usage in the final project. I don't think I really need any quotes from the LW perspective; I plan to paraphrase Yudkowsky and the Sequences as well as Dylan Thomas's poem "Do not go gentle into that good night" for the opposing viewpoint.
I don't want to go into too much detail as to what it is exactly I am working on (if I fail or lose motivation fewer people will be disappointed), but I think that the project will take a maximum of 2 months to complete. This means that it will in all likelihood be complete in 3. More details as progress is made. Thank you in advance.