Backdoors in cryptography

The concept of a backdoor has cast a shadow over the security industry for a long time. A backdoor is an intentional flaw in a cryptographic algorithm or implementation that allows an individual to bypass the security mechanisms the system was designed to enforce. A backdoor is a way for someone to get something out of the system that they otherwise would not be able to. If a security system is the wall, a backdoor is the secret tunnel underneath it (ARS Technica, 2014).

Should the US Government, and specifically the NSA, be permitted to have backdoors in cryptographic sysytems? Why or Why not?