In the episode where Wes is preparing for his Starfleet Academy entrance exam, Worf tells him that "only fools have no fear." (Presumably, he doesn't consider pre-emotion-chip Data to be a fool.)
Other than in "Night Terrors" (when he clearly wasn't in his right mind), does Worf ever admit to being fearful?
In the DS9 episode "Let He Who Is Without Sin..." Worf finished a sentence Dax started about him being afraid of losing control, saying "someone I care about might get hurt", a pretty clear acknowledgement that he was indeed afraid of this. From the transcript:
WORF: When I was thirteen, I was captain of my school soccer team. We had made the championships, and I was determined to win. Near the end of the second half, with the score tied, my team got a corner kick. The ball sailed up high. Both I and one of my opponents, a human boy named Mikel, leaped up to head the ball. He had position, but I was determined to score. I remember laughing with excitement as I threw myself at him.
DAX: Go on.
WORF: The next thing I knew, the ball was sailing into their goal. I roared with triumph and turned around to Mikel to gloat, only to find him lying on the grass bleeding. Our heads had collided when we both went up for the ball. I had not feel the impact, but I had broken his neck, and he died the next day.
DAX: It was an accident.
WORF: Which only makes it worse. Compared to Klingons, humans are fragile creatures. I realised at that moment to live among them I must practice restraint.
DAX: That must have been difficult for you.
WORF: At first. In time it became part of who I was, who I am.
DAX: And you're still afraid that if you lose control
WORF: Someone I care about might get hurt.
I would say that the episode "Coming of Age", which features Worf saying "only fools have no fear" as you mentioned, has some subsequent dialogue where he clearly admits that the fear his own psych test played on had to do with depending on others to the extent of putting his life in their hands--from the transcript:
WORF: The psych test is no more or less important than the rest of the process.
WESLEY: That's what they said, but I can't stop thinking about it.
WORF: Thinking about what you can't control only wastes your energy and creates its own enemy.
WESLEY: How can they know what my deepest fear is when I don't?
WORF: By analysing your psychological profile. They were very accurate about everyone I tested with. Including myself.
WESLEY: You? I thought there was nothing that could frighten a Klingon warrior.
WORF: Only fools have no fear.
WESLEY: I'm sorry, Lieutenant. I'm asking too many personal questions.
WORF: It is very difficult for me to depend on anyone for anything. But especially for my life.
WESLEY: But on the Enterprise you do that every day. Everyone depends on everyone else to protect them.
WORF: Yes.
WESLEY: So you overcame it?
WORF: No. It is still my enemy.
The episode that comes to mind here is Ethics. Worf winds up a paraplegic after an accident. Initially he refuses to see his son and eventually asks Riker to help him commit the Klingon version of honorable suicide. That leads to this exchange (emphasis mine)
Worf: "Will you or will you not help me with the hegh'Bat?"
Riker: "You are my friend. And in spite of everything I've said, if it were my place, I would probably help you. But I've been studying Klingon ritual and Klingon law, and I've discovered that it's not my place to fill that role. According to tradition, that honor falls to a family member. Preferably the oldest son."
Worf: "That is impossible! He is a child!"
Riker: " 'The son of a Klingon is a man the day he can first hold a blade.' True?"
Worf: "Alexander is not fully Klingon! He is part Human!"
Riker: "That's an excuse. What you really mean, is that it would be too hard to look at your son and tell him to bring you the knife, watch you stab it into your heart, then pull the knife out of your chest and wipe your blood on his sleeve."
Worf ultimately decides to pursue a risky surgery to regain the use of his legs. While not an explicit admission of his fear of having Alexander watch him commit suicide, there's a pretty obvious implicit fear expressed in that decision.
In the Deep Space Nine episode In Purgatory's Shadow:
Dax: So in other words, you were afraid I'd make a scene, that I'd embarrass you, maybe even cry?
Worf: You are capable of anything.
Aside from that, I have only found idiomatic usage of the phrase "I'm afraid", as in the novel Strike Zone:
"Lieutenant Worf, have you looked in a mirror lately?"
“I'm afraid I don't under—”
“A Klingon does as a Klingon is, Lieutenant Worf..."
And an idiomatic use in another episode of DS9 (thanks to Valorum for this one):
Sisko: We'll evaluate your actions later, old man. Right now I'd like to know everything you've learned about this Breen Dominion alliance.
Worf: I'm afraid we have very little information to share with you, Captain.
I suppose idioms don't count, so the only instance in which I could find Worf tacitly admitting to having been afraid is the first example above; he isn't afraid of injuries or death, though - he's afraid of being embarrassed.
In the Deep Space 9 episode "By Inferno's Light" (season 5), there is the following dialogue:
GENERAL MARTOK: There is no greater enemy than one's own fears.
WORF: It takes a brave man to face them.
All life forms experience fear, courage is overcoming fear. So I'd say, yes Worf does fear, but he is brave.
