Keeping Hard Copies of Receipts, Invoices, Bills, etc

Hello Guys,

Now, that we are in the digital age, where basically all your statements, credit card receipts, invoices and all that can be printed out "on the fly" and are saved in databases, is it still important to keep all your receipts, all your invoices that you receive (or send out) and keep all this paperwork? or is that just becoming such a time consuming task that it is best to not waste time/money/resources on this any longer?

Thanks in advance for your responses.