I have a lot of experience with this type of thing. Both in my personal life (my Amex card was stolen and similar events occured) and professionally as a security consultant in years past.

I can tell you with some certainty that if those items were ordered to your house intentionally, someone intended to come by and swipe them almost immediately after they were left at the door, in the event they were left at the door. That's a very typical scenario.

Definitely make a police report. Definitely.

Also, pull your credit report right away and check it for anomalies, and if necessary, place a fraud alert on it. Credit card theft is one thing, full-scale identify theft can be much more complicated. Don't panic, but keep an eye on your credit report and your other cards/bank accounts.

Check here for more info: http://www.experian.com/credit-educa...revention.html

The next thing I would do, if you are the type of person that likes to get to the bottom of things, is to look at your statement and pick out a few places that you've recently used the card at that you think might be a place someone would swipe it. Restaurants, shops at the Mall, bad neighborhoods, etc.

Go back to those places and talk to the Manager or the highest ranking person you can find (definitely not a desk employee or waiter or etc). Strike up a conversation, tell them what happened and tell them you suspect their store was where the card number was stolen. Ask them if they suspect any of their employees would be capable of such a thing or if there's been previous similar incidents. This is an uncomfortable conversation to have, and more often than you might imagine, they will tell you things.

I had this happen at a hotel. I knew my Amex was stolen either at a particular hotel or at a particular rental car agency. I went to both, and had the same conversation. The car agency didn't think it was likely, but the manager of the hotel immediately looked at me and said, "I bet I know exactly who it was."

Boom - I passed the info to the cops, guy was arrested within a week, he went to jail.

So, yes, you should be concerned that these people have your address and etc. However, the majority of the time, these are non-violent paranoid criminals who really just want to steal things, and are probably as adverse to an encounter with you as you are with them. If anything, they're usually terrified at the idea of being caught red-handed. The mere sight of you is often enough to send them running. Of course, there are situations in which this is not the case, but the point I'm trying to make is that you shouldn't be frightened. Just make a police report, get a new card number, and go about your business. Take reasonable precautions that are appropriate for your neighborhood and general safety, but don't sweat it too much.