You would have to do this on a document library basis, but you could
setup an Information Management Audit Policy in the document library.
Then you can specify what kinds of events you want to audit. This will
generate an XML file  over time of everyone who accessed  files in the
library. You could then read and analyze the XML data to find out how
often that one file was accessed.

we obtained the no of times  a file  was downloaded  by parsing the IIS LOG
using a custom program . i am not sure, but please look into the use of
LOG parser.

Where would that file  be located? Would it be accessible from the site, or would
it require server access?

The file  is on the server, but as I remember you can set the system up
to generate an excel report that is available via the site settings
page.