The packing.org site seems to be down this morning. This is an interesting question because it's one of the few areas where federal law can protect you against tyranny by a state when you are passing through.
Section 926A of Title 18, Chapter 44 of the US Code sets a standard to protect people who cross state lines with personal firearms:
[b]§ 926A. Interstate transportation of firearms
Notwithstanding any other provision of any law or any rule or regulation of a State or any political subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where he may lawfully possess and carry such firearm to any other place where he may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a compartment separate from the driver's compartment the firearm or ammunition shall be contained in a locked container other than the glove compartment or console.[/b]
(See [url]http://www.atf.treas.gov/[/url]. I searched for "Firearms Owners Protection Act")
IOW if keep the gun unloaded and either the firearm or the ammo in a locked container, no state or locality can hassle you for possessing it. You have to be travelling from one place where it's legal for you to own the gun to another place where it's legal for you to own the gun.
If you happen to be travelling only through states that allow less restrictive carry, you can carry in any manner that doesn't violate state law.
Mortech has a really good point about CCW permits. Many states respect permits issued by others, so as long as you avoid weird places like Californistan (where state law happens to be almost identical to 926A) you may be able to take long road trips properly armed. Out in the West it's pretty easy to get a Utah permit IIRC, and that is respected by several states.