It's very important to update your computer, navigators, plug-ins.... everything. Updates can add new features, but they also protect you from being infected by a virus. Using internet with an "outdated" system is THE WAY to be inefcted.
You don't have to turn it on, but at least just turn it on: "Tell me when a new update is available, before downloading it". So a message will pop up and ask you if you wanna download it, and then install it.
PS: if your navigator is really IE 6, you should REALLY install IE7 or, even better, Firefox 3. IE6 isn't safe.