Is a domain registrar, such as goDaddy, always also the hosting service, or are there any companies that just register domain names? Would a company that only registered domains be able to remain in business?

Well, many people use Godaddy not just to register domains, but also to host their websites, which means they purchase hosting from this company.

However I suggest you to read the reviews about GoDaddy's hosting services before purchasing hosting service from them.

Yes, there are many companies that have started by offering domain names only. But since domain names are so closed and related to hosting, those companies would not be very money wise not to offer hosting as well.

Saying this I'm thinking about Enom, Name.com, NameCheap, etc

Years ago, the markup on domains was anywhere from 400% and higher. Domains were being sold from $35/year and $70/year in many cases. These days with domains being sold as low as $8/year and the actual FEE ICANN charges is $6.95 there's so little markup that domain registrars have all pretty much turned to hosting, ssl certificates and other sources to suplement their income.

Thanks for clarifying this for me. I was thinking that it probably wouldn't make much business sense to restrict to domain names only, at least not at this point.

Indeed under the modern IT industry,many companies are finding the opportunity to make money or considering to expand their current services market. So as more and more domains are needed then hosting plans comes to their mind.

No, domain registrars do NOT equal hosting providers, although they can be. And I wouldn't take any free domain offers tied to hosting because you'll encounter real issues transferring that domain should you switch hosting providers.

The ICANN fee is (tld dependant) ~$0.75, I think you mean the Registry fee (which for .com as an example is to Verisign-GRS and ~$7.40)