I don't think that anyone can get a domain for free at least there must be a catch. As I know there are some places you can buy for cheap like 1and1.com.
I never heard about free domain name for sites, do they work properly in future? it is necessary to pay if you want to take a quality for your website, I think.
try go-daddy or name.com they are the best,name.com sometimes gives good discount in .com domains(i guess every friday)
Nothing is cheap, but you can require cheaper and quality. lol Free international domain is not impossible, if you buy hosting, guys may offer you free domain registration as a gift, or you register a bunch of domains at one time, you can ask for a discount, then, one or two domains can be free in this sense. Just try it.
if you find cheap domain you can find on go daddy, it's cheap for dot info domain for the first year just $0.89, but if you looking for free domain, you can try .co.cc
theren are many godaddy coupon, just googling with keyword "godaddy coupon". in the past i found cheapest discount, with about 7 dollars for .com domain. yes for the cheapest dot info : godaddy, and for .org domain let's try name.com
Is http://www.dot.tk/ a free international domain? I'm not quite sure what the intended meaning of "international" was.
If you want free you have to settle for something like what SwimFinn has suggested dot.tk but since its free you are never in control, they can yank it from under your foot anytime and since its free you cant even complain. Try the above and see if thats what you want. Otherwise try to send $x and get a domain, consider it as a business expense. You cant start a business without spending anything maybe you can but you wont get anything back. If its just for a blog or something, then you can try wordpress.com / blogspot.com/ posterous.com. www.posterous.com has some nice feature. Ani
Look out for the special promotion by domain registrar...there always have great offer for domain name. I bought .info last few years for just 0.99. Well it depends on what you want to use the site for. If it's for your main business then go for .com (going to cost you around $8).
You could use Wordpress.com for a free presence on the web though the web addresses all end with wordpress.com for example YourName.wordpress.com There are lots of similar sites, but dont think you can get a specific web name for free.
You should use subdomains like co.cc or co.nr if you want to not pay for domain. If you look cheap domain visit domainsarefree.com or use this coupon "DOLLARDOMAIN" at netfirms.com
I use Godaddy for my domains. A domain isnt that expensive, and only a cost each year. The hosting will be a recurring cost, but look for a decent host who may offer a free domain as an incentive.