Q:

How do Protestants understand the blessedness of Mary in Luke 1:48?

What are the common Protestant interpretations of Luke 1:48?

Luke 1:48 (KJV) For he hath regarded the low estate of
  his handmaiden: for, behold, from henceforth all generations shall
  call me blessed.

In each of their generations, how is Mary called blessed to the fulfillment of this scripture?

A:

For most Protestants this is a matter of semantics. Protestants know full well that Catholics call Mary, the "Blessed Mother." They also know that if you ask a Catholic "Is Mary blessed?" They would surely answer "Yes, indeed she is." But the Catholic should understand that the Protestant, in general, would also answer the same. Mary is blessed. Mary received a blessing beyond compare to any other: She bore to us our Lord and Savior. The Son of God calls her Mother!
Protestants, however, do not venerate Mary as the Catholics do. In fact, Protestants mostly have a great disdain for veneration of any saint, thinking it akin to idolatry. As an effect, most are wary to assign such titles to any saint, living or dead. They typically stop at Pastor and other lesser priest-like titles, and naturally those are for persons actually holding the office. So what we have is that Catholics literally call her "Blessed" and Protestants call her blessed when describing the nature of her relationship with Christ.
Cynics, who may or may not be Protestant or even Christian, may also note that this might be a case of a self-fulfilled prophecy. Mary said people would call her blessed. People agreed, namely the Church, and started calling her blessed, literally.

A:

I'll supplement fredsbend's accurate answer with Protestant commentators on this verse.  They agree that Mary was blessed, both in that she was selected by God to be the mother of Jesus, and in the spiritual blessings she, as his follower, received.  Thus Mary's character ought to be remembered and emulated, but only because it is an outworking of God's grace in her life, not because she in herself is worthy of praise.
Protestants argue that Mary's "low estate" refers not to her own humility, as Origen and others have it, but to the lowliness of her condition.  Calvin writes:

By calling herself low she disclaims all merit, and ascribes to the undeserved goodness of God every occasion of boasting. For ταπείνωσις, lowness, does not here denote [...] “submission, or modesty, or a quality of the mind,” but signifies “a mean and despicable condition.”

This is important because it guides how Mary is considered "blessed."  Rather than seeing God selecting Mary as a reward for her humility, Protestants like John MacArthur argue that Mary understood that she owed everything to God:

She doesn't say all generations will look to me to bless them.  They'll consider me blessed because of what I’ve received.  [...]  It is the Lord whom her soul magnifies in verse 46.  It is “God my Savior” whom her spirit exalts in verse 47.  She sings of the great things that God has done, verse 49, “for me.”  Great things God has done on her behalf.  She rejoices in the great mercy God has shown her.

Thus, Mary's blessedness is seen as one of many manifestations of the blessings of God.  John Wesley sees Mary's rejoicing as primarily a response not to being the mother of Jesus, but to her hope of salvation in him, which she shares in common with all believers.  Albert Barnes argues that "it is right to consider her as highly favored or happy," on account of her being the mother of Jesus, but compares her blessing to that received by others – Abraham as the father of God's chosen people, Paul as the apostle to the Gentiles – and concludes that, like them, she ought not be worshiped or prayed to.  
As Calvin writes, venerating a person, rather than God's work in that person, misdirects praise that is due to God:

Let us remember that, in praising both men and angels, there is a general rule laid down, to extol in them the grace of God; as nothing is at all worthy of praise which did not proceed from Him.

Of course, Protestants praise her example – John MacArthur calls her a "model believer" and a "true worshiper," while Calvin calls her "holy" and "our teacher."  For this evidence of God's work in her, and for the honor of being selected as the mother of Jesus, is she blessed.

Barnes, Notes
Calvin, Commentary
MacArthur, "Mary's Praise", March 28, 1999 sermon.
Wesley, Notes

