Some people say very good things about GoDaddy as hosts (not as domain registrar, which is a different thing) and others hate them. The same with quite a few other hosting companies. Your choice would also depend on what *you* need and your website administration experience level. For instance, if you nothing about webservers, you might want a lot of customer support and handholding and when you don't get it, you might think the hosting service bad. On the other hand, if you are a webserver expert, you would only want the servers to be maintained and administered well by a company and you would know how to do all the rest. So, your expectations determine how good or bad a host is, to an extent.
Additionally, the host you go with would also be determined based on how much you are willing to spend, the level of control you require and the features/functionality that you expect. I believe you have specified the latter to an extent but you haven't mentioned if you need PHP, mySQL or any other extra features. If you don't, and price is a consideration, you should be able to get a basic site with about 500MB - 1GB of space for about $5 a month. Or, you can go a bit higher and get your own virtual private server (VPS) for about $20-$40 a month. The advantage of a VPS is that it's a self-contained virtual server that you can manage on your own - you control what's installed, what's not installed and so on. But, you have to have the Linux knowledge to do that.
The best thing would be to check out a forum like WebHostingTalk (
http://www.webhostingtalk.com/) for hosts in the particular category you're interested and make your own decision based on the feedback provided by others. If there's a specific host you are interested in and they don't have any feedback on the forums, you can even start a new thread asking for feedback.
ETA:
Since this question comes up about once every month, I'm sticking this thread and changing the title slightly so that others can find it easily