Ohh! I know! I know!
There are two states that allow concealed carry without: an application, a permit, any testing, fingerprinting, etc...; just as a resident of the state you have this right.
Vermont and Alaska
As far as I know, VT does not issue CWP's. If you can own it, you can carry it, period. However, their statutes do not have a preemptive statement (I think that's what it's called?). Their counties/cities/towns/etc can restrict CC to the point of it being illegal in their respective jurisdictions.
Alaska adopted the VT method with a few modifications. They implemented an availability of CWP's in order to establish reciprocity (sp?) with other states. Alaska also included a preemptive statement (again, not sure if that's the right term) that says something to the effect of 'Citizens have the right to carry a concealed weapon, and that right shall not be infringed by any municipality.' As far as I know, municipalities may restrict open carry, but no city/town/borough/etc can make CC illegal. Alaska also extends this right to all non-residents. However, you must be a resident of the state to apply for a CWP.
"To preserve liberty, it is essential that the whole body of the people always possess arms, and be taught alike, especially when young, how to use them." -Richard Henry Lee, Virginia delegate to the Continental Congress, initiator of the Declaration of Independence, and member of the first Senate, which passed the Bill of Rights.