Here are the current standings By state regarding gun permits (in short and this can change at anytime based on new laws and amendments signed into effect both federally and by individual states):
No-Issue: A No-Issue jurisdiction is one that does not allow any private citizen to carry a concealed handgun. The term refers to the fact that no concealed carry permits will be issued (or recognized). States Included: Illinois, Wisconsin, District of Columbia
May-Issue: A May-Issue jurisdiction is one that requires a permit to carry a concealed handgun, and where the granting of such permits is partially at the discretion of local authorities (frequently the sheriff's department or police). The law typically states that a granting authority may issue a permit if various criteria are met. States Included: Alabama, California, Delaware, Hawaii, Iowa (On April 29, 2010 Iowa governor Chet Culver signed SF 2379 into law on January,1 2011 Iowa will become a "Shall issue" state), Maryland, Massachusetts, New Jersey, New York, Rhode Island.
Shall-Issue: A Shall-Issue jurisdiction is one that requires a permit to carry a concealed handgun, but where the granting of such permits is subject only to meeting certain criteria laid out in the law; the granting authority has no discretion in the awarding of the permits. Typical permit requirements include residency, minimum age, submitting fingerprints, passing a computerized instant background check, attending a certified handgun/firearm safety class, and paying a required fee. States Included: Alaska, Arizona, Arkansas, Colorado, Florida, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Maine, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Mexico, North Carolina,North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee,Texas, Utah, Virginia, Washington, West Virginia, and Wyoming.
Unrestricted: An Unrestricted jurisdiction is one in which no permit is required to carry a concealed handgun. States Included: Alaska (is both a Shall-Issue and an Unrestricted state), Vermont (is unique in that permits are not required for both resident and non-residents to carry concealed), Arizona (On April 16, 2010, Arizona Governor Jan Brewer signed legislation allowing for unrestricted carry. The law will take effect 90 days after the end of the state's current legislative session, putting the effective date on July 29, 2010).