Where should I register a domain name?

I will be needing to register a domain name in the very near future. Do you have any recommendations to point me to the right company? Is there a certain company that I should use for a business site (as compared to a personal site where nobody gives a rip where it's registered)?

I did manage to register a few not too long ago with godaddy, but I've been doing some reading and it looks like this might not be a good idea in some cases. I don't want to do anything illegal with a domain name, but it seems that they have a pretty open policy that allows them to suspend names without much consideration.

I'm also in the market for a hosting company. Lots of space and bandwidth are needed. I'd rather have a great company to work with than a cheap one, but any opinions/pointers that you can offer will be appreciated.