if u mean .com, .net , .org, .eu, .my and etc, impossible there will be free one. even if there has free one, it will register under those registery name rather than ur and it will free for limited time like one year only. unless u win from particular content that org by someone
Some companies offer a free domain name when you buy hosting...pay for hosting but domain name is free (though you still have to pay for something, so not completely free).
1 and 1 dot com they give you a free . com, at least since last month all you need is a cc hope it helps