There are 2 websites.
www.jigokutsushin.net is a fake jigoku tsushin. you can access the website anytime from anywhere.
www.jigokutsushin.de is the real jigoku tsushin. you can only access the website at midnight. any other point in time, the "404 Not Found" will appear, which is the same website on the show.
Neither of them are real. www.jigokutsushin.de is just more realistic. If you change your computer time to 12:00 it will open. After you type someones name in, its pretty obvious its a game.