Nowadays, we don't have price tags on anything anymore. Prices are fetched from a database using the UPC as a key, so if the computer's down, the buyer is out of luck. At a previous employer, we sold specialty goods to contractors, so we had strong relationships with our customers. I drafted a plan to print up pads of paper sale forms that looked more or less like our (80x24 greenscreen) order screens, so if we lost connection to the mainframe, we could still move product from the warehouse to the customers; we'd just give them the product and bill 'em later. It was a risky move, but not really any riskier than sending our customers across the street to our competitors. To my knowledge, they've never had to use the manual system, thankfully.
We may not be "completely dependent on computers" just yet, but we seem to be getting there.