Yes, however there are things to consider.
The very first thing you need to consider is hosting. This refers to the location your web site files are stored, they must be accessible via the web. There are hundreds of options, each with its own restrictions. You can create your own web server, but this is very advanced and depends on your computer being on and connected to the internet always.
Creating your own web server:
Be the Master of Your Own Domain With a DIY Webserver - Wired How-To Wiki
Most free systems come come with restrictions and services. The restrictions often include bandwidth, content, advertisement, and number of services. The services available will have to match your needs. For instance a site coded with ASP needs to have management access to ASP services. One coded in PHP on the other hand will need to have PHP available.
Free webhosting:
Top 10 Free Web Hosting sites
This brings me to content. You can use a website builder, which often comes with many hosting packages available, even free ones. You can code your own site, but if you are not well versed in 1 or 2 scripting languages this can take some learning. There are other options that are far more versatile. They have free CMS (Content Management Systems). CMS systems are generally well coded and can be used for a variety of applications. They take a little know how to install but come with great documentation and tutorials. They also usually have community support and development you can access.
http://spyrestudios.com/free-content...ement-systems/
The other simple alternative is to use a website template. This is a basic website that you can use by changing colors and pictures and layout if you are well enough versed.
Free Website Templates
This brings me to my last point of consideration: the domain. With free hosting you are generally given a sub-domain. So if you host at x11s.org you can choose from several domain options.
<yourchoice>.x11s.org
<yourchoice>.freehosting.org
etc.
They often let you take a domain you own and point it to their website. TLD's or Top Level Domains are structured like <yourchoice>.com .org .gov etc. They gennerally cost money, however this is very little. For a low traffic domain at godaddy.com you only pay somewhere near $12 a year. There are however some neat emerging options. Some extension offer free domain registration such as .co.nr and .nf.
Best Free Domain Name services
I hope this has been helpful.