Depends on the state. Some have laws against having uncased firearms, even if unloaded, in the driver/passenger compartment.
In Wisconsin it is now legal to openly carry a handgun in a car without a permit. But the weapon must be in clear view and only pertains to handguns, not long guns.
Would be against the law in Minnesota. Permit allows open or concealed carry of a handgun in a motor vehicle. Long guns must always be unloaded, cased and in the trunk or non-accessible place.
Here is an active map showing CCW reciprocity agreements. I can’t vouch for its accuracy.
As pkbites said, it depends on the state. Just to give a different example, in Pennsylvania we don’t really have “concealed” permits. We have what is called a “license to carry firearms” (LTCF). You technically don’t really need an LTCF to open carry, but the police may harass you a bit depending on where you are. With an LTCF you can carry a concealed handgun, so in that respect it functions like a concealed carry permit. Also, if you open carry and you have an LTCF, the police won’t harass you as much (even though the open carry bit isn’t part of the LTCF). The law isn’t written that way, but for all practical purposes, the LTCF basically says you can do whatever you want (with a few restrictions, of course). An LTCF also allows you to carry a loaded handgun in your vehicle. Concealed carry permits in some other states don’t allow this.
In PA, you don’t need an LTCF to have a gun rack and long guns in the vehicle. However, the weapon must be unloaded. I don’t think it’s a legal requirement, but the general rule is if you leave the action open so the police can see it’s unloaded they’ll leave you alone. If the action is closed you may get pulled over so they can check to make sure it’s unloaded.
Unloaded long guns in a gun rack are legal in OH and WV as well. I believe it’s not legal in NY.
I really appreciate most of the feedback I got here. Thank you. In fact I’m in love with some of you. 
Now on The Kid’s behalf: A shotgun or youth rifle? Same laws? (Clearly not CCW)
Already covered. Long gun. Cased, in non-passenger accessible location in vehicle, ammunition stored separately.
You can carry any firearm across state lines (yes, any) with the proviso that you follow the laws of your destination once you arrive there and you do not stop for any significant length of time in a jurisdiction where the weapons in question are illegal. This is covered by the Firearm Owners Protection Act of 1986.
As an example, I live in Pennsylvania. I can take an NFA weapon (full-auto) through New York City on my way to Vermont, where possession of said weapon requires no permission, as long as any stops I make are transient in nature. If I get a hotel room I can be arrested. If I get gas or a quick bite to eat, as long as I have the weapon properly secured they can’t do a thing about it even if the weapon is illegal as hell for an NYC resident to keep.
In that respect CCW laws differ significantly. If you carry a concealed weapon under the same circumstances and you are caught you will be arrested. The safe harbor provision only holds for properly secured weapons and for short periods.
EDIT: engineer comp geek, you cannot openly carry in Philadelphia, a city of the first class (and the only one in PA), or in vehicles, without a permit.
This used to happen in Wisconsin also. I frequently told other cops that it wasn’t going to end well for them if they didn’t knock this shit off, but some people insist on learning the hard way. Even after the Attorney General put out an opinion that open carry was legal and protected under the state constitution some officers continued to harass OCer’s.
It always ended with any charges being dropped or the individual being found not guilty, and a civil lawsuit being won by or settled with the open carrier. The lowest payout was 7K, the average is 30K!!!
Last November when the CCW law finally went into effect the state statutes were written to reflect that open carry was legal, even without a permit. The Disorderly Conduct statute had a sub section added to say that open carry is not illegal, is not disorderly conduct, and cannot be prosecuted, not even as an ordinance violation citation.
Good!