It's funny, the songs I have in mind aren't actually about some*thing* to fear, they just seem to mostly be about fear itself, and the hold it has.

"Cold and Ugly" by Tool and "Carondelet" by Ruby seem to be mostly about the same thing, which is the fear of opening oneself to the inner truths, to the chaos that is just below the skin. In some ways it is the fear that we all have, of losing control, and letting go of any ability to save ourselves and going exploring into the most dangerous parts of ourselves.

Cold and Ugly
Tool

Underneath her skin and jewelry,
hidden in her words and eyes
is a wall that's cold and ugly
and she's scared as hell.
Trembling at the thought of feeling.
Wide awake and keeping distance.
Nothing seems to penetrate her.
She's scared as hell.

I am frightened too.

Wide awake
and keeping distance from my soul.
I am scared like you.

Carondelet
Ruby

I feel like burnin' this town
This face is bringin' me down
I feel like breakin' this town
This fear is burnin' me now
How can you live with this shit goin' on
I feel like burnin' this town
My fear is walkin' around

How can you live X3
Now, now

To be there is all I could do
Is that so wrong
Just one care is all I could find
Now it's gone
I'd open my heart just to see
What's inside
A mountain of raw that's too
Big to hide

How can you live X3
Now, now

When I say I love you, I know that I lie
But it feels so good to scream it out loud
At least I try
This fear, this fear is burnin' me now
is that all I can get now?
This fear, this fear is bringin' me down
I know it's not mine
This fear, this fear is breakin' me down
It's all wrong
This fear, this fear is bringin' me down
is that all I can get now?
My fear is walkin' around

How can you live X3
Now, now
To be there is all I could do
Is that so wrong
Now
Just one care is all I could find
Now it's gone
Now
I'd open my heart just to see what's inside
Now
A mountain of raw that's too big to hide
Now

Then there's the fear of stuff we should be afraid of - stuff that's out in the big bad world. Sometimes you can only justify so much about what you can do, and then self-protection has to start taking a more offensive stance.

Big Exit
PJ Harvey

Look out ahead
I see danger come
I wanna pistol
I wanna gun
I'm scared baby
I wanna run
This world's crazy
Give me the gun

Baby, baby
Ain't it true
I'm immortal
When I'm with you
But I wanna pistol
In my hand
I wanna go to
A different land

I met a man
He told me straight
"You gotta leave
It's getting late."
Too many cops
Too many guns
All trying to do something
No one else has done

I walk on concrete
I walk on sand
But I can't find a safe place to stand
I'm scared baby
I wanna run
This world's crazy
Gimme the gun

Obvious Answers:
Tori Amos: Mother
TMBG: Spider