I have a couple stories:
I had my credit card number stolen online about 15 years ago. I think it happened when I tried to buy something online. Since it was a fake order site, they had my credit card, full name, and address. I discovered it when I got a billing from a web hosting company. Since he used my info, I was able to retrieve the admin info from the hosting company. The site wasn't used yet, and I was able to get the site shut down and was refunded.
I consider myself lucky. Since he was using my info, my identity would have been attached to this future scam site. Could have caused some real problems for me. I am just glad that it happened before "paperless" billing was the norm.
You also have to watch out for your parents. A couple years ago, I my dad was living with me. I was helping take care of him as he is older and has health issues. One day I came home from work and he was reading off all his credit cards to someone on the phone. He had a lot of credit card debt, and someone had called him offering to "help". Luckily I was able to help him contact all the credit card company's and get the numbers changed before anything happened.
Years ago, I received a letter that I was denied a credit card for a store card. It was for a card I did not apply for, for a store I never heard of. I called to investigate. They used my name and address, but did not have my SSN. I did check my credit history, but there was no trace of it. I tried reporting it to the police, but they said that it was not id theft since they did not use my SSN and the only info they did use was public record out of the phone book.
More recently, I have received several calls from "Microsoft Windows Support" from MSC, and apparently I have an enforcement action out for me from both the IRS and the marshals office. I never have been home for the IRS or marshals office scams. I always thought it would be fun to mess with them for awhile. But I have for the Windows scammers. I just which they wouldn't call after 10pm.