Outside the University, there are plenty of free email services that you can subscribe to. For example, MSN HotMail gives you webmail-like access to an inbox and many other features, for the price of looking at advertising when as you read your email. Google's Gmail has less obtrustive advertising, a bigger inbox, but fewer features and a simpler interface. .
An external mail account can have significant advantages:
it won't expire when you leave the University.
it's independent of the University, and mail sent to it can't be easily read by the Uni.
There are also disadvantages, though:
if something goes wrong and an important University email is lost, it's your responsibility.
you are dependent on the service to be reliable and always available.
Remember though, that most official emails are only sent to your University address, so you'll need to forward those emails on or regularly log into both accounts.