About Domain Lagoon's free domains:
I have two from them(and a hosting package) and they have been GREAT. I have had them for a little under a year now and I'm loving it. The only problem I've ever had was that there was this one server crash...And uh, everything kind of died...But some people found out how to go back and get their databases/files from the old servers...After that they switched to Cpanel make daily backups so that is no longer a problem. If you just get a domain it will be in your name and they'll have nothing to do with it. If anything, I would DEFINITELY recommend it, it's very good. Also, I have a referral code so that's another reason...>_>
You can also pay with any of the *lagoon services they offer. I hate to whore out my code but PM if you're interested...
/rant
Of course there are plenty of other options for you to choose from. In the free zone, DL is the best I've seen (and believe me I looked).
If you feel like paying, there's a lot of cheap sites, try stuff like Servage or Yahoo. Actually, don't go with Yahoo, they're paid hosting sucks. But if it's only a domain you want, GoDaddy is a pretty good option...