Yep, I use GoDaddy. I don't know whether they're the cheapest, but the hosting and domain names are reasonably priced... and they're also been around for quite a while, so they seem pretty reliable.
I'm on the cheapest plan ($3/month) and got a domain name for an extra $2 (a year). That wasn't too bad, considering the plan includes email addys, PHP, MySQL and there's no ads.
The only negative I've noticed is that their website is really cluttered, which is annoying when you're navigating around and trying to change your hosting setttings. If you're only wanting a domain name, though, it probably wouldn't be as much of an issue for you
Edit: I just remembered another positive feature. GoDaddy is teamed up with a company called
Domains By Proxy, which means you can register a domain name under their name and address instead of your own (for an extra yearly fee). This was good for me, because my parents really wouldn't like the idea of their postal address being on the internet!