If you use Apple Mail, the files you want to backup are in your Home folder, under Library. Please be careful in there! That is where the Mac stores all your user-specific settings and preferences, so if you move or delete anything then your Mac will not behave as it used to.
If you use Microsoft Entourage, you need to backup the folder called Microsoft User Database found at Home > Documents. You may also wish to migrate your email into Apple Mail. Of course, we can help with that.