I live in Pennsylvania which is a "shall-issue" conceal carry permit state -- if you can pass the background check, you can get one. Some states, like RI apparently are "may-issue" which is at the discretion of some politician or law enforcement official. Some states (like Vermont and Alaska) are conceal carry free -- you don't need a permit at all. Alaska also has a "shall-issue" permit process allowing state residents to carry in other states that allow it.
Many states allow "open carry" -- that it is legal to carry an unconcealed firearm without a permit. Pennsylvania is one of those (except in "cities of the first class", Philadelphia). However, except way out in the boonies, if you did walk around suburbia with a firearm unconcealed, you'd get hassled constantly because of the calls the cops would be getting "man with a gun".
- David