This article is from the Paper Money Collecting FAQ, by Bruce Giese email@example.com with numerous contributions by others.
To keep them in the best possible condition you should use Mylar holders.
Common household products such as plastic wrap, plastic bags, window
envelopes, etc. should not be used for storing paper money. Most
plastics contain PVC, which deteriorates with time and heat, releasing
acids and gases which will migrate into the paper, resulting in the notes
appearing to have been soaked in oil, or so brittle they shatter at a
touch. Use only those products (such as Mylar and other inert plastics)
which have been tested and approved for long term paper money storage.
Notes should be stored or displayed away from direct sunlight, to
avoid fading. Repairs should be made only with products that are stable.
"Magic" tape and other plastic tapes will leave permanent stains on notes.
There are individual Mylar holders which look like plastic
envelopes and cost about 30 cents each, usually in packs of 50 or 100.
You can also keep notes in regular paper envelopes as well, although
they're more liable to get damaged in handling.
If you really want to get fancy, there are special albums with
associated Mylar holders. Each page holds 1, 2, 3, or 4 notes
(there are 4 different types of pages). This stuff is made by
a company called Lindner and it costs more than the individual
holders. I believe the album and 20 pages cost around 60 US dollars.
Additional pages are something like 20 dollars for 10. You can fit
maybe 50 pages in one album. Unfortunately, Lindner made the pages
so they would only fit in their album. Theoretically you should
use both the individual Mylar holders and the Lindner pages, but
for anything worth less than 20 dollars, I just use the pages.
They're a lot like Mylar.
Most big-time dealers carry Mylar holders and Lindner albums.