American law thinks in terms of rights. Jewish Law, halachah, is much more comfortable speaking in terms of obligations than of rights. In the case of the Danish Cartoons, I think there's something to be learned from the differences.
I would argue that the halachic concepts offer some advantages over the American ones. They could be compared to an intersection, where truck meets pedestrian. Under the American system, where each presses his rights, the truck driver frequently ends up in jail and the pedestrian in traction. Under the halachic system, with each mindful of his obligations, you may wear out your brakes a little more quickly, at the savings of a great number of collisions.
In American terms, there are two conflicting rights: freedom of the press and the "right" not to be offended. In Jewish terms, there would be two complementary obligations: the obligation not to offend and the obligation not to behave like a beheimah when offended. You could therefore argue, as Hugh Hewiit and other have, that both sides are wrong, although now with the die cast, we need to defend press freedom.
Or, you could argue, as I do, that that all works as long as you're in a civil society. But once one side starts to play chicken, pretending to step off the curb in order to get you to slow down, things change. There's no sanction for the other guys trying to enforce your obligations by denying theirs, to back you off by threatening violence. Muslim groups, even Western ones, have been playing chicken with the press and public officials for too long now.
To put it back in American terms, I'd take a third alternative: absolute right-of-way. At roundabouts, or traffic circles, one side has the absolute right of way. In America, if you're on the left, you win. It means you're in the circle, and you get to go where you want, ahead of the guy entering the circle. (Exiting, of course, there's no collision.) Since I don't really believe in the right not to be offended, I'd give full preference to free press, and to expect the insulted groups to get the address right for their protests.