Every now and then, I encounter someone in a panic about the fact that a website they've surfed to knows their IP.  This panic often results in the discovery of various anonymous web surfing services (sometimes called proxy servers)  that purportedly allow you to browse the web without anyone knowing who you are.  Now, everyone is welcome to be as paranoid on this topic as they choose. I will note, however, that in my opinion, most of the paranoia on this topic is rooted in a total lack of knowledge on the part of the paranoid.

Every web server has always been able to see the IP address of every visitor. This has been true from the beginnings of the web and is fundamental to TCP/IP. It has never changed.  When you browse to a website, what is actually happening is that your DNS subsystem resolves a canonical/host name (like www.regnatarajan.com) to an IP address, and then your networking subsystem initiates a connection to that IP address -- in the case of an HTTP connection, it usually connects to port 80. The web server on the other end usually allows that port to be opened and sends back responses to the requests made by your system.

This is always true. There is no other way to browse to a website hosted on a web server, and all web sites are hosted on web servers of some kind or other.  There are minor variances to the mechanisms described above, such as entering the IP address directly in the address line, but these result in the exact same thing minus the DNS resolution and they don't change the basic principles involved. Now, here's the important part: as soon as this connection is open, the web server knows your IP address. Every time.  It has to, or it wouldn't know where to send back the responses.

Every web server you connect to knows your IP. Deal with it.

Now, anonymous web surfing services simply introduce a layer between you and the web server. You connect to the anonymizer service, it connects to wherever you want to go, and it passes the information back and forth like a relay agent. The web server only sees the anonymizer's IP and you never connect to the web server directly so you're anonymous, right? Wrong. You are simply now trusting the anonymizer service with your security instead of the web server, which is usually highly dubious. The CIA is strongly suspected of operating many of the popular anonymizer services, and some others are operated by kids and hobbyists who I, personally, wouldn't trust at all with my personal data. I know this to be true as many of them rent servers from my company to do it. Beyond this, any anonymizer service in the US, even if it honestly intends to be credible, is subject to the Patriot Act which allows government to inspect the service's logs and data and forbids that service from informing its clients that this has happened.

Now, if there's a site you particularly distrust but need to access, using an anonymizer service may be a credible thing to do in that case, but don't delude yourself into thinking you're anonymous. You've just shifted your vulnerability from one party to another.