no-ip is pretty sweet service. Depending on what kind of connection you have (Static or Non-static) the availibilty of your site will differ.
If you have static (your ip address never changes) you can choose either to give out the ip address as your web address or use no-ip's service to get a url. Your website is on as long as your computer is on and apache is running (assuming that's the program you use)
If you have a non-static connection (Your ip address changes every time you reboot your modem and/or pc). You now cannot give out an ip address, because it changes, but no-ip will solve that issue, because they have a free software that pings the server to tell them of an ip change if necessary, so your website will be restored within 5 minutes.
And finally, no-ip is free if you use a sub-domain. (ie. tugmistress.no-ip.com they have many master domain names to choose from so be sure to check it out).