Think of it, you connect to a web server and want information sent to you, like the pictures and text of the web page, if the server does not know your IP address how is the information going to reach your computer
Indeed, the website will always see an IP adress if you connect to it. Now, you can use software or proxies that effectively change your IP by acting as a waypoint between you and the site, but since the proxy still knows your IP, and most proxies leak data, chances are the site will still find out your IP if they really want it. But since that wasn't what you asked...
