Since Emacs 21, there's been a module named 'newcomment, which has different comment styles (see the variable 'comment-styles.  This setting gets close to what you want:
(setq comment-style 'multi-line)
(Note: you should probably make that setting in 'c-mode-hook).
However, none of the settings make the comments look like what you want.
The easiest way I saw to get what you want is to add this hack:
(defadvice comment-region-internal (before comment-region-internal-hack-ccs activate)
  "override 4th argument to be just spaces"
  (when (eq major-mode 'c-mode)  ; some condition here
    (let ((arg (ad-get-arg 4)))
      (when arg
        (ad-set-arg 4 (make-string (length arg) ?\ ))))))
The current settings for comment-style always prefix the comment lines with " * " (if not the whole " /* ").
If you don't have Emacs 21, I suppose you could simply download newcomment.el from the repository.  I don't know if it works as-is in earlier versions of Emacs, but it might be worth a shot, though upgrading Emacs would be a better solution.
My hack breaks the 'uncomment-region.  A proper fix would be to change 'comment-padright.  That would take a little more research so as not to break other things.  The above hack only changes behavior in 'c-mode (adjust the condition to your liking).