HostGator is widely considered the leading service in the web hosting business. They are offering all range of hosting related services, from shared environments to high-performance dedicated servers. The prices for shared hosting are a little higher that the competition, but for extra one or two dollars per month you get the highest quality of service and user support. You can also save a lot if you pay for long term and use one of the available coupons. For long term purchase HostGator is really cheap.
They are also offering domain registration service, but the control panel of domain management is not very easy to use.