I don't mean any subdomains,directories or anything like batcave.net, geocities.com. I mean domain name registrations such as .com, .co.uk, .org etc but for absolutely free.

No! You can only get free sub domains! Somebody has to pay for the registration!

Yes.

http://office.microsoft.com/en-us/office...

The domains such as .US are available for free. They're also a bit clumsy because of the way they are regulated.

Yes. You can get a free domain at http://www.dot.tk. But they do not offer any space for hosting your webpages, that means they just let you use a URL like "www.my-name.tk" and all traffic to this URL will be forwarded to your actual webpage which may be hosted on any free webhost of your choice. That's the best you can get for free!