I find it difficult to believe that you guys know of sites that were ranking for competitive keywords that never engaged in any type of SEO. With all due respect and without wanting to offend anyone I think it's a ludicrous claim.
@irishsolar I mentioned it earlier, but I'll repeat it since this thread is so long. I help manage a friend's old FrontPage Express site. It's a horribly coded mess, lots of dead outbound links, and she really hasn't updated it in years and couldn't care less. Yet, her site is unquestionably the leader in her niche and traffic just keeps going up, up, up. That in itself says to me that SEO doesn't carry much weight when up against an authority site. If your site is popular, the search engines will rank it warts and all.