Scripture refers to an unpardonable sin in Matthew 12:31–32, Mark 3:29–30, and Luke 12:10, as well as Hebrews 6:4–6.
There's also "sin that leads to death" (1 John 5:16–17).
Given the Protestant understanding of sin, what is an overview of the doctrines they develop from these passages? To Protestants, what is the unforgivable sin?
Related, but not tradition-specific: What is the blasphemy of the Holy Spirit?
Protestants basically fall into three main camps, claiming that the unpardonable sin is:
Within (3), there are three views regarding who can commit the sin: 3a) only the regenerate (saved), 3b) both regenerate and unregenerate (unsaved), and 3c) only the unregenerate.
(1) Some, particularly dispensationalists like Lewis S. Chafer, take the view (also held by Jerome and Chrysostom) that the unpardonable sin could only be performed during Jesus' time on earth, since the sin specifically "consisted in asserting that Christ’s works, which were wrought by the Holy Spirit, were accomplished on the contrary by Satan."1 Charismatics like J. Rodman Williams similarly view it as the "utterly perverse ascription of the work of God to Satan," but argue that it can still be committed today.2
(2) The second position was held by Augustine,3 some early Lutherans, and several Scottish theologians. One of the latter was Thomas Chalmers, who writes that "it is a sin which can be charged upon every man who has put the overtures of forgiveness away from him." Expressing his disagreement with other views, he writes:
So that this sin, looked upon by many as the sin of one particular age, or, if possible to realise it in the present day, as only to be met with in a few solitary instances of enourmous and unexpiable transgression, is the very sin upon which may be made to turn the condemnation and the ruin of the existing majority of our species.4
(3) The third position is held by later Lutherans, Arminians, and Calvinists. The Lutherans espouse the first subdivision, the Arminians the second, and Calvinists the third.
(3a) Lutheran John Mueller explains that the sin is "committed only when the Holy Spirit has clearly revealed the divine truth to the sinner and the sinner nevertheless utters blasphemies against it."5 He notes that most dogmaticians6 in his tradition "teach that the sin against the Holy Ghost can be committed only by those who were regernerated," with the exception of those who argue that it can also occur in the unregenerate "in the very moment when the Holy Ghost is about to convert them."
(3b) The second subdivision, that either regenerate or unregenerate can commit the sin, is held by Arminians. Jacobus Arminius described the sin as the "rejection and refusing of Jesus Christ through determined malice and hatred against Christ [...] against conscience."7
(3c) The third subdivision (only the unregenerate commit the sin) is believed by those in the reformed tradition, like John Calvin and Louis Berkhof. Calvin writes that the sin is committed by those "whose consciences, though convinced that what they repudiate and impugn is the Word of God, yet cease not to impugn it,"8 but that "he who has been truly regenerated by the Spirit cannot possibly fall into so horrid a crime."9 Berkhof's definition reads:
The sin consists in the conscious, malicious, and wilful rejection and slandering, against evidence and conviction, of the testimony of the Holy Spirit respecting the grace of God in Christ, attributing it out of hatred and enmity to the prince of darkness.10
Notes and References: Berkhof and Combs provide helpful summaries; Combs in particular includes additional quotes, including some from church fathers and medieval theologians, and a review of how modern theologians fall into the camps above.
Agreeing mostly with point 1 in Nathanial's answer, though it requires a bit of clarification and expansion because as with most groups, dispensationalists (myself included) are not monolithic. We do tend to be an exception to the general protestant rule of Bible interpretation in that we first look at whom a given letter was addressed before deciding if and how its content applies. Through that lens, we're convinced that Hebrews was written to exactly whom the supplied title of the letter indicates. It was not written to the Body of Christ in which there is no longer any Jew/Gentile distinction and in which all sin has been forgiven (Rom 8:1; Col 2:13), its members guaranteed be kept safe by God unto glory (Rom 8:28; Phil 1:6). Rather, it was written to group that could taste the things that accompanied salvation but were still at risk of falling away through faithlessness. Those were Jews, just as the author indicates throughout the book.
However, there is not full dispensational agreement on WHAT that unforgivable sin entailed. Some do say as pointed out in Nathaniel's answer while others believe it involved rejecting Christ as Messiah, which most of Israel of that day did. One line of reasoning here (which I share) is that the Jews allowed John the baptizer (the voice of the Father) to be killed. Then, they demanded Christ Himself be killed (though He asked they be forgiven for they knew not what they did). Finally, Stephen, of whom it was pointedly said "was full of the Holy Spirit," was brutally murdered by Jews' own hands (Acts ch. 7). It was shortly after that point we see the unexpected salvation of the vilest human enemy of Christ, the persecutor Saul, who as Paul was sent forth unto the world with the previously unrevealed Secret (mystery) that Israel was now being set aside and all mankind could come to God directly through Christ without any national or human intermediaries.
And why? Because the covenant nation Israel not only refused to repent, she blasphemed the Holy Spirit by murdering Stephen. That, some of us believe, marked the blasphemy that would not be forgiven, and it also coincides with the historic beginning of the end of God's dealings with her as a nation.
As to the original question:
To Protestants, what is the unforgivable sin?
The only "unforgivable sin" believed by most dispensationalists (and many non-dispensational protestants) to exist during this dispensation of God's grace is to die after having heard and understood the Gospel of the grace of God, but rejecting it. For that, there is no remedy.
