Fear is one of Sauron's primary weapons in The Fellowship of the Ring (though he also likes to exploit people's pride, arrogance, and anger when he can). As soon as the Black Riders start appearing, the first thing anyone mentions is that they are frightening. When the Black Riders attack Frodo, Merry, Pippin, and Sam at Weathertop, Merry and Pippin both throw themselves to the ground in horror, and Sam can't lift a finger to fight them. Clearly, the agents of Sauron use fear to their advantage: they are, literally, terrorists. Does the Fellowship have tools at their service to combat this fear? What protection is there against the deadly fear of Sauron's servants? (Bonus question: Do you think Tolkien's sensitivity to the inevitability of fear in horrible situations is the result of his own familiarity with fighting in the trenches of World War I?)
If Sauron were not around, there would be nothing to fear in The Fellowship of the Ring.
In this novel, there is no shame associated with fear.