What Are the Best Web and Email Hosts?

GreyPoopon asks: "My wife has been running a small business for a couple years now. She is currently paying for web hosting services for a domain, but has elected not to put up a web site (she doesn't need more business), instead using the service only for sending and receiving email. Recently, the hosting service has become less and less responsive, and attempts to switch monthly bills to a different credit card have been completely ignored, and she's now looking for a new provider. She's interested in both hosting service providers as well as email-only providers that will allow her to use her existing domain name with up to five mailboxes. What are the best choices, these days?"