There are quite a few ways people can block Caller ID. When someone chooses to block Caller ID, what it basically means is that his or her call will come through as "Unknown Caller," "Private Number," "Unavailable," et cetera, on the Caller ID of whomever he or she is calling. While some companies - especially telemarketing companies - fraudulently block or "spoof" their Caller ID, there are a variety of reasons why someone may want to do this to his or her outgoing calls.
The first way to get your Caller ID blocked is to call the phone company for the phone which has the number and information you want blocked. Most land line companies, cell phone companies, and VoIP companies offer the option of blocking Caller ID, many of them at no extra charge. If you are ever calling a number from which you do not want your information and identification to be blocked, there are several codes you can punch in first to disable Caller ID Block, for just that call. The most well-known are *82 and *65.
If, on the other hand, there are only some people from whom you want to keep your information, you can dial in the code *67 and your Caller ID will be blocked for that call - so, for the next call you make, if you do not first dial the code, the Block Caller ID feature will be disabled. When using this code and the aforementioned two, it is important to remember to dial the code, then 1, then the area code, finally followed by the number.
Another option used to block Caller ID is using call diversion, also known as Operator diversion. To use this method, all you have to do is dial 0 for the operator and request that he or she place the call for you. Using a prepaid phone or dialing card causes Caller ID to be blocked, as well. There are also companies which offer to block Caller ID for people who call through them - you are generally charged per minute. Of course, you could always use a public phone, too!