Modern Encryption
As modern encryption techniques develop, it seems that code breakers have gone to extraordinary lengths to break them. The following "unbreakable" systems have been documented as exploitable.
AES Encryptions Broken
Although much more secure than their DES counterparts, the AES Encryption has shown to be exploitable as well. The Wi-Fi Encryption Scheme (WEP), is a modern day AES system that has been broken. In 2005 the FBI held a demonstration where they broke into a WEP network in 3 minutes.
Content Scrambling System
This system, which is used in all DVD's and DVD Players is a hold over from before 1996 when the government regulated the length of encryption keys, and has been broken on countless occassions.
GSM Communications
GSM Communications are the encryptions used by A5/1 and A5/2 cellphone roaming networks, which 98% of all cellphones are on, have also been cracked.
Current State of Computing
In a PBS Frontline Interview, John Arquilla put it best, "The strongest computer in the world is not a mainframe being manufactured in the United States or Japan. It's the parallel computer being hotwired by a hacker from some dusty office in some abandoned building."