Own domain even with free hosting providers
Most free hosting service providers, like Tripod and Freewebs, don't let you choose your own domain for your free website. Your domain will be something like "username.tripods.com" or "www.freewebs.com/username". This of course, is not quite as nice as having your website located at "www.yourdomain.com". Most of the free hosting providers allow you to have your own domain with their paid hosting plans, but then of course this is not free hosting anymore...
Since writing this information I have actually found a free web hosting provider that does let you use your own domain name. The hosting is free and without ads, but you will need to register your domain with a domain registrar as usual. Luckily a domain registration with a cheap registrar, like GoDaddy, doesn't cost nearly as much as paid hosting. So this might be a really good alternative for many of you.
The free hosting provider that enables you to have your own domain name is: www.4realhost.com.
If for any reason you wish to use a different free hosting provider instead of 4realhost, here are some tricks you can use to have your own domain with any free hosting provider. You can even do it completely free.
Completely free domain - dot.tk
You can register your own domain from www.dot.tk completely free and forward it to your free hosting account. You can only get domains ending with .tk, like "www.yourdomain.tk". This domain will be automatically forwarded to your free hosted website and it is automatically masked. This means that the browser will actually show "www.yourdomain.tk" in the address field instead of your hosting providers address (like "www.freewebs.com/username").
Here is an example. I have a free website hosted at Tripod. This website is located at http://owndomain.tripod.com.
I have also registered a free domain from dot.tk - "www.owndomain.tk" and forwarded it to the Tripod website. And it looks like this:
This used to be a really nice deal (for a free service), but now when there is the redirecting page, it basically spoils the whole thing.
In addition to the usual problems with domain forwarding with masking, you can't configure your dot.tk domain to having a "redirect 301" server header. Basically what "redirect 301" does is tell the search engines that this domain is only an alias and not duplicate content (which the search engines don't like). But if you only have one extra domain pointing to your free website, this should not be a problem.
The cheap version - real domain registration
If you don't like your domain ending with ".tk" or any of the other limitations of dot.tk domains, you will need to register a domain from an ordinary domain registrar. You can get a ".com" domain from GoDaddy for $8.95 per year (not month, but per year), so it's really not that expensive either.
You can then have this domain redirected to your free website with or without masking. With GoDaddy you can also set the server header to "301 redirect" (so that the search engines don't penalize you for having duplicate content on several domains). And if you later want to change your hosting provider or switch to a paid hosting service, you can easily set up this domain to be used with your new hosting package.
Still, even with a paid domain registration using domain forwarding is never quite the same as having your domain properly set up with your hosting provider and configured in their DNS (Domain Name Server). Read more about these limitations from problems with domain forwarding. I therefore highly recommend using a hosting provider that allows you to host your own domain. Usually free hosting providers don't offer this, but as I said before, there now seems to be atleast one that does: 4realhost.com.
Domain forwarding and website templates
Another possible problem with domain forwarding can come up when you are using the website templates from your free hosting provider and you have more than one page. The home page of your website is not linking to the other pages using your forwarded domain - instead it is linking to it's own web address. When your website visitor clicks on any of these links, the browser window might "forget" your forwarded domain and show your website providers domain instead. Whether this happens or not depends on how your free hosting provider is configured. If it uses relative urls for linking to each page, then everything should work correctly. Absolute urls on the other hand will start showing your hosting providers address. Different free hosting providers handle this differently, so you just have to see how it is with your website.
If you can configure all your links to point to different pages on the forwarded domain, the browser will keep showing this domain. For example "http://www.yourdomain.tk/secondpage.htm" instead of "http://yourdomain.tripod.com/secondpage.htm". You will probably not be able to do this when you are using the automatic website builders offered by free website hosting providers.
Popular Web hosting providers
which offer multiple domains
on a single hosting account:
IX Web Hosting
Go Daddy Web Hosting