I was wondering if it was possible to buy a domain name rather than to have to pay for it every month.

What happens if you stop paying your host site ? Is your whole site deleted ? For example, I have my site about Japan hosted free on Lycos. If I decide to pay Lycos to get my own doamin name, avoid the ads and speed up the access to the site (is there any other substantial advantages by the way ?) and then want to stop paying for it later ; what happens to my site and domain ?