Why use them? Because they give you an instant view of useful information. You can summon them, learn what you want in a glance, and then dismiss them.
My favorite widgets are actually two weather widgets. One gives me the a quick 5 day forecast for my area, the other contains a weather.com derived real time moving weather radar for my area. I check them both multiple times a day. It is simple stuff like this that is really useful.
I also have a stocks widget, so that I can check how the stock market is doing every now and then, and then of course there is the invaluable iStat Pro. You can summon up more information about the current state of your Mac than you ever thought you would need, until you see it the first time of course. How hot are your CPUs? How fast are the fans turning? What is your IP address? All of this is available in this one widget.
The wonderful world of widgets is indeed wonderful. Try them out and you will quickly find them invaluable. Even Microsoft finally got the message, and embodied in their vastly inferior Gadgets implementation in Vista.