Is it possible to customise SharePoint search so that certain documents in a Document Library could be given greater weight in search results based upon whether or not they were flagged (by adding an additional column) as important?
It might not be completely what you are lookin for but SharePoint offers a functionality called "Authoritative Pages".
Authoritative pages are those that link to the most relevant information. Search uses this list to calculate the rank of every page in the index. There might be many authoritative Web pages in your enviornment. Type the most valuable in the topmost text box. You also have the option of specifying second and third-level authorities in the lower text boxes. Enter one full URL per line. Example: http://intranet/site-directory.html.
You can specify the authoritative pages on "http://ssp/admin/_layouts/editrelevancesettings.aspx"
I'm not sure if you have looked at Best Bets as a solution, but I figured I'd throw that out there and see if you have tried that. Here's a few links to get you started: