To control how things are displayed in dired, you can customize the variable dired-listing-switches.  However, as you noted, not displaying the number of links is not an option.
A slightly different approach would be to use the package dired-details, which hides all details until you want them.  This hides the number of links (but also hides other information).  Follow the link to find the package (and a dired-details+ which sounds like it fixes a couple minor inconveniences with dired-details).
Original answer information follows:
(setq dired-listing-switches "-l")
From the "Entering Dired" info page:
The variable
  dired-listing-switches' specifies the
  options to give tols' for listing
  the directory; this string must
  contain -l'.  If you use a numeric
  prefix argument with thedired'
  command, you can specify the ls'
  switches with the minibuffer before
  you enter the directory specification.
  No matter how they are specified, the
  ls' switches can include short
  options (that is, single characters)
  requiring no arguments, and long
  options (starting with --') whose
  arguments are specified with='.