I was at the National Archives and Records Administration a few weeks ago, which is way more awesome and less boring than it sounds: it's where they keep the actual, real, original Declaration and Constitution (and Bill of Rights)! You can go right up to them, and even see the signatures. I'd recommend a trip to anyone visiting DC, and it's like a block from the Smithsonian Natural History Museum. The rotunda with the documents is a museum, so it includes some political as well as physical history of the documents.

For the Declaration of Independence, the very short version is: The Revolution was a hectic time, and the Continental Congress were technically outlaws, so it was rolled up and carried around in a wagon for a while. After government was established, it went back and forth between a few bureaucracies except for one wild wagon ride in a cloth sack during the War of 1812. Aside from writing it on Parchment (which I think is durable), there didn't seem to be much preservation effort for a few decades until it started visibly fading. The full history of the physical document is available online, and I'd recommend reading the whole thing because it's pretty interesting.

http://www.archives.gov/exhibits/charters/declaration_history.html

I've tried to find the same info for the Constitution and Bill of Rights on that site, but no luck so far.

Along those lines, did the founding fathers think that the "original documents" would be held in such high regard, hundreds of years later?

About a year ago I wrote this response which detailed where each of the Declaration of Independence, Constitution and Bill of Rights has been in their histories. As you can see, they spent much of their time in the State Department followed by the National Archives.