In one of the papers I read last week, someone received notification from the National Health Service about appointments which they hadn't made because, as it turned out, NHS had incorrectly assigned the same ID number to 2 people. The "victim" didn't know how much of his medical history had been mixed up as a result of this. Of course, NHS didn't explain how this could happen or what they were doing to find any other duplications!
Also on the radio over the weekend, there was an item about someone who received text message 'reminders' that his Barclaycard was overdue for payment. The problem? He'd never had a Barclaycard in his life, but, being blind, these messages could be read out by text-to-speech software at the most inconvenient times. Barclaycard were unhelpful, because they claimed that the only person who could ask for the mobile phone number to be changed was the owner of the account (although they now claim to have amended it).
And this is without companies and government officials just 'losing' entire copies databases!