that Tolkien has included several characters who make up their own minds as to whether "orders" apply in a difficult situation.  In Rohan Hama sums up the Rohirric attitude, in a line borrowed from Beowulf by saying that a "man of worth" has got to be able to weigh things like this up on his own.  To pick up wajeff's point about the Nuremburg trials, no Rider by this reckoning would ever think to excuse himself on the plea that he was "just following orders."  At any rate, Hama lets Gandalf takes his staff into Meduseld; Hama also gets ahead of his brief when he brings Éomer his [Éomer's] sword before Théoden says to do this.  Éomer, meanwhile, decides, against orders, to let the Three Hunters pass and even to give them horses.  Finally, a naturalised Rider, Merry, disobeys a direct order from Théoden and tags along on the ride to Gondor. 
     The situation is different in Gondor where people are used to treating "orders" as "orders" and not questioning them.  Most of Denethor's servants do obey his final commands.  Still, Faramir has decided to violate a standing order by letting Frodo and Sam go; and Beregond too will violate orders.  Even here men of worth eschew blind obedience. 
     To refer again to wajeff's point: I doubt that Tolkien thought that "following orders" was much of an excuse for wrongdoing; and Tolkien stood much closer in time to a spectacular example of a principled refusal (one would like to think by men of worth) to accept this as an excuse.

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.