This topic has grown very quickly, and there are many people saying a lot of different things. Rather than try to address everyone, I'm just going to stick to some general information about this kind of hack.
What has undoubtedly happened in all these cases is that your Apple ID has been hacked. How that may have happened, I don't know. It could be weak passwords falling to brute force attacks by a botnet. It could be that people "logged in" to a malicious fake Apple server in response to a phishing e-mail. It could be something else entirely.
Once the hackers have access to your Apple ID, they can remotely lock all your iOS devices with a message. They can also see any data stored in iCloud (calendars, contacts, e-mail, notes, etc). If you have a Mac with Back to My Mac enabled, they could potentially get remote access to that. They could also make purchases on your Apple ID.
The solution to the problem is to regain access to your Apple ID. (Erasing the device is not a solution in many cases.) Reset the password, and make sure to change it to something very secure. As an additional security measure, I strongly suggest that you enable two-factor authentication on your Apple ID. Doing so provides additional security, and should prevent the hacker from ever being able to take control of your Apple ID entirely away from you.
A couple things that it's important to understand:
1) It is entirely possible for a hacker to lock you out of your Apple ID permanently by changing your security questions or even enabling two-factor authentication, which would prevent you from resetting the password. If the hacker enables two-factor authentication, Apple will not intercede to give you access! This is a security measure for people who choose to enable this feature, since you wouldn't want a hacker to talk an Apple support rep into giving up access to your Apple ID.
2) If you have iOS 7 installed, and have chosen to turn on Find My iPhone/iPad/iWhatever, a hacker in control of your Apple ID can lock you out of your device permanently. You will not even be able to erase the device without providing the Apple ID password. If they manage to take control of your Apple ID permanently, then you obviously will not be able to do that any longer. Apple will not give you access to a device locked in such a way, as this is an anti-theft feature.
You should not be afraid of turning on Find My iPhone, which is an important anti-theft feature. Instead, simply enable two-factor authentication to make sure your Apple ID is secured, so nobody can manage to use this feature against you.
Note that enabling two-factor authentication does not guarantee that your Apple ID won't be hacked, so you still need to use a strong password. What it does protect against is changes to your Apple ID that would give the hacker permanent access. With two-factor authentication enabled, you will always be able to reset the password on your Apple ID and regain access to it, as long as you follow the directions and are careful to save the recovery key.
