This is one of those things where I always wonder why people would use a free e-mail service such as gmail or hotmail as their primary business e-mail when they already have their own website and could literally create any e-mail account using their own brand/identity. It seems like you are wasting a bit of free advertising as well by not using your own e-mail brand such as when you pass off business cards.
I think the most common reason I have heard is that most free e-mail addresses are web based and so you can access it anywhere at anytime without the need of say a desktop that has an e-mail client like Microsoft Outlook or Mozilla Thunderbird. There are a lot of options though if that is the only reason that you are using a web based e-mail. For example, I know of companies simply install open source web based e-mail programs on their site such as a program called Squirrel mail at http://squirrelmail.org/. With that people can access their mail on the road with a desktop based e-mail client and when they get home or at the office they can do things like usual.
I personally just find that you have more to gain by trying to use your own e-mail a much as possible if this is for business purposes.