I think it is a good investment.
You can get an 8-Sheet-at-a-time shredder
for a reasonable price.
It's nice to have in an accessible, convenient corner of your home office or work room. Just shred bills or bank statements as you get them, but pay and read them first :)
Another alternative is a shredding service. My local Kinkos does not offer shredding, but my local Office Depot does- at only 99 cents per pound. Use a shredding service for big jobs.
The next alternative is getting statements and bills online. It saves trees and frankly, it's where commerce is going!