Proper preservation of papers that make up a family history collection is often neglected by many people.  These papers could be printouts from your computer, newspaper clippings, birth/death/marriage certificates, old report cards, mom's love letters, and so forth.  A little bit of care is all that is needed and you'll greatly increase a document's longevity.  After all, we want them to last so our descendants can enjoy them.  Its not hard either, here are some tips:

1. Most paper contains acid, which over time will cause the paper to weaken and become brittle.   Newsprint has an especially high acid content, which is why your old obits, birth announcements and such become brittle quite quickly.  All is not lost though, for documents that are on acid-bearing paper, spray them with a deacidification spray, such as Archival Mist.  This is by far the best and easiest method to neutralize the acid.   But you can make your own dipping solution:
   • Mix 2 tablespoons of milk of magnesia to 1 quart of club soda.
   • Allow the solution to refrigerate at least eight hours before using.
   • Put the solution into a pan that is large enough for the clipping to lay flat and be covered by the solution.
   • Soak the clipping for 1 hour.
   • Wet paper is very fragile, so carefully remove the clipping from the pan and place it on a soft towel to dry.
   • Be sure the clipping is completely dry before moving.

Always test an unimportant clipping in this process as many inks are water soluble.  Inks have been known to entirely disappear from paper during this process.

2. After you've made your documents and clippings acid free, store them in acid-free and lignin-free albums, archival boxes, or page protectors.  Make sure the papers, especially newspaper clippings, are stored flat and not folded.  While you can laminate newspaper clippings after you de-acidify them, be cautious as the heat could cause long term damage.
3. Print out your computer data on acid free paper.  There are many suppliers of this (Great White, for example) and you can buy it at an office supply store.  But don't let the paper come into contact with other acid bearing paper/materials because it will contaminate the paper.  Most printer inks are acid-free, but they are not waterfast.  So put your print-outs in archival page protectors to protect them from accidental spills and to minimize any handling damage.
4. If you are putting items in a scrapbook or heritage album, mount them on acid-free, lignin-free paper with an acid-free adhesive (you may want to use small amounts of adhesive on the edges of the document to allow easier removal if needed later).
5. For your very important documents and newspaper clippings, you might want to wear gloves when handling them to keep your skin oils from staining the paper.
6. Pens with acid-free ink or pencils should be used if your going to write on a document.
7. Avoid long-term exposure to light as the UV rays can cause damage.  High heat and humidity are also detrimental.
8. Use a pH test pen if you have any question as to whether a document is acid free. For pH pens to work, though, water must be present to show the shift in color. Newsprint, for example, tends to be a particularly dry paper. So if you are testing newsprint, you may have to place a drop of distilled water on the pH pen marking to see the color shift.
9. To repair a torn or ripped document, use an archival, transparent document mending tape (such a made by 3M).  Do not use typical cellophane tape.

Some related links:

Library of Congress information on paper preservation:
http://lcweb.loc.gov/preserv/care/paper.html

Guidelines for storage from the State Library of Victoria, Australia:
http://www.slv.vic.gov.au/slv/conservation/flatpapr.htm