Paper is, all things considered, pretty stable. Unlike digital material, it can sit on a shelf for many years and still retain its structure, shape and information (this is typically referred to as "benign neglect" in jargon-y terms). That said, paper does degrade. Ever pinned a newspaper clipping to a corkboard or fridge in the direct sun and realized a month or so later that it had turned yellow and crumbly? This is the work of heat (such as sunlight) and humidity interacting with the lignin in the paper. Lignin is a compound found in trees and that can be quite prevalent in ground-wood pulp paper, such as the paper used to print newspapers.
The paper used to print books and pamphlets and even office paper all contain varying qualities of paper depending on it composition, when it was produced, and the processes and chemicals used in its production. The condition of items depends on the quality of its paper, the manner in which it has been treated and stored, and the use it has seen. Sometimes, despite our best efforts at intercession, items in our collection deteriorate.
We recently had a researcher ask to see a pamphlet. It was readily apparent that this pamphlet was in very fragile condition. It was incredibly brittle and crumbly, and sections of pages were missing. A quick search of WorldCat revealed that only 3 OCLC member institutions held a copy of this pamphlet, and a quick search of our own catalog showed that the author was rather important (we hold 57 other works by him). The pamphlet, then, was both relatively rare and fairly important. It was also highly likely that even with careful handling, this pamphlet would only last through one other researcher — perhaps two, if we were lucky.
It was readily apparent that something had to be done to extend the life and usefulness of the item. Here at the Congregational Library, we evaluate situations like this with emphasis on retaining the informational value of an item and providing access to that information, and so we prefer to migrate (more jargon) that fragile document to a new format that is more likely to last longer. Once upon a time that would have meant photocopying the original (we even have several examples of this process in our stacks); today it means digitizing it and making the pamphlet available on the web. This has the double benefit of providing what we refer to as a "reader's copy" (a copy of an item that is not the original, but that is made available to a reader in an effort to preserve the original) and making the item accessible to researchers who are unable to visit us in person.
It should be noted that digitization does not mean that we will get rid of our original copy. One of the best principles of preservation is that "lots of copies keeps stuff safe." Digital copies of things actually require more work to preserve than physical copies, most of the time, and so best practice dictates that we keep both the digital copy (for readers to look at) and the physical copy (as a sort of back-up).
If you are interested in preserving your old paper, we recommend keeping it in a stable environment that does not change overly much in humidity or temperature and that is generally dry.
If you are so inclined to digitize your papers, we encourage you to keep your "hard copy" original, to scan at a fairly high resolution (350-500 dpi), and to maintain a back-up of your digitizations in a physical location that differs from the physical location of your computer or hard drive.