While it has never happened to me personally, it is a massive threat and there are simple things people can do to prevent it.
The main thing you can do, is shred important documents and letters and old credit/debit cards. The Fellowes Powershred DS-1 shredder if is perfect for just that.
Set up and operation are really straightforward. Whilst it does come with a manual, it's so easy to use, you probably won't need to look at it - I didn't! Setup took like 30 seconds. Out the box, plug it in and you're ready to go! All you've got to do is switch it on and put the paper in it and it's shredded! You really can't get much simpler than that. Then you can rest in the knowledge that no-one is going to be able to steal your details. There's a reverse switch in case something isn't feeding properly or you suddenly spot you're shredding something you need as well. It automatically stops when it has finished shredding, but if you start to feed paper, it senses it and starts up again. It has a long 4-5 minute continuous use before it shuts down allowing you to keep shredding for longer.
I must say, I think the shredder is very stylish - it's not an eye sore to have in your home - it's a nice black with a stylish 18L mesh pedal bin. The bin pops out easily to allow you to empty the contents too.
You can see a video of the Fellowes Powershred DS-1 Cross-Cut Shredder in action here.
All of my important documents and letters now get shredded without any thought.