Try joomla.org (very powerful mysql data website). Just say you want to change your template, no worries, just click your chosen default template and the entire site's template can be changed.

Or if you're into blogging, wordpress.org is good. A very powerful blogging tool.

Would you have your own domain and host? There are free hosts, but these two are good if you want to load them onto your host and make your own website yourself.

Google offers the 'Google Sites' a free and easy way to create and share webpages. Below mentioned URL offers the free sites from Google:

http://sites.google.com/

Check and enjoy.

You can't make any website for free. Even if anyone provides such a service they'll have lot of restrictions.

However you can make a blog for free. but your domain name will be yourname.blogspot.com(if you do it with blogger.com) yourname.wordpress.com (for wordpress.com) or go with tumblr.com ( yourname.tumblr.com)

Try Dzite.com