Yes, you could. You could then either give your friends the IP address of your computer and have them use it in the URL instead of the domain - a la http://11.22.33.44/your/web/site/index.html - (this works best if you have a static IP address, one that doesn't change over time), or you could use a dynamic DNS service such as www.no-ip.org to get a free subdomain and have it point to your IP address. I think there is a Linux client for no-ip's service, so that would work even if your IP address changes. Or you could do both.
"Those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety."
-- attributed to Benjamin Franklin
www.dyndns.org is another, I have actually had better experiences with no-ip but I'll just throw it out there and let you choose. Some home routers like Linksys and Netgears have built in support for dyndns. That may or may not be an issue for you.
I cant get the no-ip client to work in Gentoo. I installed it from portage, but when I run "noip2 -C", nothing happens. It just stucks there and I have to break it with Conrtol + C. After that, there is some noip..... file in /etc/ director, but it's empty. Can anyone help me with this? I've used no-ip addres in Windows for sime time now, and I wouldn't like to change this.