"I must not fear. Fear is the mind-killer. Fear is the little-death that brings total obliteration. I will face my fear. […]" (1.83)
One of Dune's all-time classic lines. The line shows that, in a way, fear is the main antagonist in Dune, as it's the greatest obstacle standing between Paul and his goals.
"There were water riots when it was learned how many people the Duke was adding to the population," [Jessica] said. "They stopped only when the people learned we were installing new windtraps and condensers to take care of the load." (8.78)
Along with the gom jabbar, this quote points toward one of the pivotal fear primers in Dune—the fear of pain and suffering. Death by dehydration wouldn't be our choice of exit strategy, so we can understand the people rioting.
Please permit the [conservatory] to convey a lesson we learned from the same teachers: the proximity of a desirable thing tempts one to overindulgence. On that path lies danger. (10.39)
On Arrakis, you even need to be afraid of yourself. Overindulgence in water, food, or pretty much anything can weaken you. Arrakis is a lot like Sparta in this regard. The weak? They don't do so well.
For the first time, Paul allowed himself to think about the real possibility of defeat—not thinking about it out of fear or because of warnings such as that of the old Reverend Mother, but facing up to it because of his own assessment of the situation. (12.217)
Paul takes that Bene Gesserit mantra and runs with it. Paul cuts through his fear with analytical thinking. This will eventually become the key to his entire success.
"I make a point," the Baron said. "Never obliterate a man unthinkingly, the way an entire fief might do it through some due process of law. Always do it for an overriding purpose—and know your purpose!" (26.115)
One man's fear is another man's democracy. Here, the Baron seems to almost fear the due process of law. After all, that pesky law might interfere with his scheming.
One could be alone out here, [Jessica] thought, without fear of someone behind you, without fear of the hunter. (29.11)
The political system in Dune is messed up. How messed up? Jessica is on the most godforsaken planet in the universe, but she can only think about how nice it'll be to not get stabbed in the back.
Something fell soundlessly past their eyes into the mice. There came a thin screech, a flapping of wings, and a ghostly gray bird lifted away across the basin with a small, dark shadow in its talons. (29.143)
The Atreides House's crest is a hawk. Paul's Fremen name, Muad'Dib, means "mouse." Is there a bit of symbolism on the nature of fear going on here, or is it just us?
There was no past occupying the future in his mind… except… except… he could still sense the green and black Atreides banner waving… somewhere ahead… still see the jihad's bloody swords and fanatic legions. It will not be, he told himself. I cannot let it be. (33.187-188)
Paul's ultimate fear is not himself or his enemy but the jihad that might start in his name. Know what the scariest part is? He can't do anything to stop it. It's like one of those snowballs in a cartoon. Not only will it grow bigger as it goes, but it'll consume him as well.
That which makes a man superhuman is terrifying. (35.223)
In Dune, characters fear what they don't understand. But sometimes, it's exactly what they understand that terrifies them more. They know what it means to be superhuman; it means that person could easily destroy them.
"The eye that looks ahead to the safe course is closed forever," Paul said. "The Guild is crippled. Humans become little isolated clusters on their isolated planets. You know, I might do this thing out of pure spite… or out of ennui." (48.159)
Paul's ultimate victory comes not because of his ultimate weapon—the spice—but from the fact that he can instill fear in his opponents. Fear of Paul's ultimate weapon becomes the ultimate weapon. You just don't mess with Paul Atreides.