Short Answer: Yes, the "fear of death" refers to being afraid of physically dying, as shown by the context in which it is used. The point is that Christ's solidarity with His people gave His people hope, thereby freeing them up to live the life He was calling them to without concern for what it might cost them. The passage is not about unbelievers and whether they are willing to die for a cause.
Since you're asking this question on BiblicalHermeneutics.SE, let's put theology and personal observations on hold for the moment and just look at what the author was attempting to communicate in the text. (Aside from site restrictions, that is just good practice in general when interpreting a passage.)
In order to determine how the author is using this term "fear of death," we're going to want to pay careful attention to the clues from the context of this speech-act. I will start with the big-picture and move down through the layers of context to that specific instance of the term. (Since this is not a Christian site, I'll skip the context of Redemptive History, and of the complete canon.)
1. Purpose of the complete literary work
Hebrews was most likely written around AD 68 to Jewish Christians of Hellenistic influence. This was a time of great persecution and trials for those of the Christian faith. Hebrews was a "word of exhortation" (13:22) to these Christians to persevere and continue in their decision to follow Jesus no matter what it cost them.1
2. Function of the passage in the literary work
The passage (2:10-18) serves to:
(A) expand on v.9, which says that the Son was made lower (i.e. human) so that He might taste death for everyone, and
(B) introduce the bulk of the work (Ch. 3-10), which presents Jesus as our High Priest.
3. Purpose of the passage:
The purpose of this passage is to show that it is was necessary for the Son to have solidarity with the people of God in order to be their High Priest. Here are a few examples from the passage:
since the children share in flesh and blood, He Himself likewise also partook of the same, that through death He might render powerless him who had the power of death -14
He had to be made like His brethren in all things, so that He might become a merciful and faithful high priest -17
since He Himself was tempted in that which He has suffered, He is able to come to the aid of those who are tempted. -18
In other words, the author is showing that it is because the Son become like the children of God that He is able to come to their aid.
It is important to note that the author is emphasizing that the Son became like the children of God -- not like unbelievers. For example, consider the author's choice of words in the following verses: "sons" in v.10, "brethren" in v.11, "brethren" and "congregation" in v.12, "children" in v.13 and v.14, "descendants of Abraham" in v. 16 (cf. Gal. 3:6-9), "brethren" and "the people" in v.17.
4. Function of v.15 in the passage:
The NLT does a good job of conveying the author's flow of thought in v.14-15:
Because God’s children are human beings—made of flesh and blood—the Son also became flesh and blood. For only as a human being could he die, and only by dying could he break the power of the devil, who had the power of death. Only in this way could he set free all who have lived their lives as slaves to the fear of dying.
What the author is saying here is that Jesus had to come in the flesh and die (thereby breaking the power of death) before He could free those who had lived their lives enslaved to the "fear of death." (Remember, the children are in view here, not the unbelievers in general.)
Exegesis: The referent
Keep in mind that Jesus died, and many of His closest followers also died. The author of Hebrews is well aware of this. This is not a claim that He set the children free from the expectation of physical death, but rather, that He set them free from the "fear of death." How did He "set them free from the fear of death"? Both the author and the readers were familiar with the Gospel message -- namely, that Jesus not only died, but also rose from the dead. This is a big deal to the NT authors. For example, at one point Paul exclaims:
if the dead are not raised, not even Christ has been raised; and if Christ has not been raised, your faith is worthless; you are still in your sins. . . . If we have hoped in Christ in this life only, we are of all men most to be pitied. But now Christ has been raised from the dead, the first fruits of those who are asleep. -1 Corinthians 15:16-20
. . . Therefore, my beloved brethren, be steadfast, immovable, always abounding in the work of the Lord, knowing that your toil is not in vain in the Lord. -v.58
The NT writers held Jesus' resurrection from the dead as the reason for their willingness to live the Christian life of persecution and self-sacrifice. It is precisely because Jesus rose from the dead that the early Christians were not afraid to die. Likewise, the author of Hebrews is explaining that Jesus had to come in the flesh and die so that He could set the children free from their fear of death -- so that they could live a life of following Christ without concern for what it may cost them.
What about those kamikazes and suicide bombers?
Though this is less of a hermeneutics question, there are several important notes to make about the exegesis of the passage as it relates to these two examples:
The author of Hebrews is presenting the Son of God as one who became like the children of God so that He could help the children of God... the unbeliever is not in view here
In this passage, the author of Hebrews focuses on Christ's ability to come to the aide of those children who face what He faced. There is no indication that the children will not face these things, or that they will not have to experience these things -- the indication is that Christ is able to aide the children when they face these things
In this passage, the author of Hebrews is presenting Jesus' conquest as a means for helping the children. The point is not really that "everyone fears death" or even that "no follower of Christ will ever fear death." The point is that Christ is able to aide those children who are facing what He faced (e.g. death)
So, in summary, I don't know if every unbeliever is terrified of dying. What I do know is that the author of Hebrews wants his readers to know that the believer has nothing to fear when faced with death, because he can hope in Christ, since Christ also faced death and conquered it.
1: Dr. Thomas L. Constable, Notes on Hebrews: 2013 Edition, http://www.soniclight.com/constable/notes.htm (accessed February 6, 2013), 1-4