An email address...but why?
Today, email has become one of our preferred communication channel. With social networks, they have almost completely replaced the phone, fax and postal mail (with exceptions).
Most people find it easier (and faster) to request information about a product or a service and receive plane or concert tickets by email.
Thus, an email address under your domain name is essential. It also looks and sounds more serious and reliable than a generic Hotmail or Yahoo address. I am not saying that you should not own that kind of email but it's better not to use it for your business.
Keep in mind that «your professional email is like a handshake to your clients» and, in this context, should appear as much "businesslike" as possible.