Hey Exciter, I could give a number of examples like live support offline/online, drop down content and logins or dynamic content. It adds some life to the page allowing for interacting without the need to continually navigate or re-download content. Tool tips and admin panels alike use it to provide live feedback (green/red/amber ticks boxes) editing such as on wordpress for creating posts... the list is literally endless.
Although JavaScript can be disabled so the site should function perfectly with and without it, and many do go overboard though a good user can allow good interaction with your user and keep them interested as well as providing much needed accessibility options for certain users (text size, polarise and imageless buttons for example)