Shredding document's does NOT prevent Identity Theft
The vast majority of computer Viruses will rob your pocket. Whether they steal the login details for your online banking website; record your credit card info when you make an online purchase, or just plain out scour your emails for personal info - they get the job done cheaply and safely for identity thieves.
It's worth noting though that The amount of money criminals are making from online consumer fraud is growing in volume every month and in double digit numbers. Though it's probably an underestimate, criminals made at least $120 Million during October, November, and December of 2009.
So don't stress about shredding everything you thow out . Stress about whether your computer has a virus or not instead.