The most important web-related crime in our society today is identity theft. This is a sort of crime that can impact anyone, seemingly at random.
Identity theft is not confined to the internet, but the internet makes it much easier to do. The fact that we can have our identities stolen relatively easily does not have a huge impact on us day to day. It does make us spend money on things like antivirus software, but it does not really inconvenience us much. However, when our identity is stolen, then we have huge problems. It forces us (and the credit card companies and others) to go to great lengths to fix the problems caused by the people posing as us. In the most extreme cases, it can ruin our credit ratings, which can be a severe problem for our lives going forward.