Your programs leave traces of what You do and the browsers history shows what sites you been visiting. If you are sharing a computer, then that might not be something that you want others to see. Even if you are using different accounts this is not very well protected in a system like Ms-Windows. It is quite easy to check what pages and web-sites has been accessed.
Your computer literate kids might be able to check the web pages you visited the day before.
A browser like Opera can clean your cache when you exit the browser.

There are some other things that you can do as well.
One way to be sure that you don'n leave any traces of this kind is to let each user have it's own encrypted disk on the computer, where you install a "private" browser (like Opera) and some stand-alone email program (like Thunderbird or pooka) that can easily be configure to store mail and settings in a specific directory on that disk.
Even if you do all this you still may leave traces in your computer in the form of temporary files, cookies, cache files, and information in your swapfile.

To clear out all the traces of what you have done, You have to clean that up manually or use a "cleaning" program to do that for you.

If you use a computer at work to look for a new job, send job applications, or something else that is not exactly in your work description, you should use an "anonymous server" service likeAnonymizer.com
These services differs a little but most encrypts the traffic between your PC/browser and the anonymous server, and then makes the request for you, and transfers the information to and from the web transparently. These are not a free services and there are a couple of providers on the net. There are also some free anonymous proxy servers on the net, but often a little hard to find and use and slow.

You should neither send your private mails from york work if it is of a more sensitive matter. This is true even if you use encryption for your emails. Very few people do, even if there are quite secure and free software available that helps you do just that.
See my selection of Software for the references