Mary being a perpetual virgin is a dogma within Roman Catholicism and Eastern Orthodoxy, and was a doctrine that many of the Reformers and their followers held to, too (e.g. Luther; Zwingli; Francis Turretin), and many Anglicans and Lutherans still hold to this belief in modern times. The historical Latter-day Saint view is that normal sexual activities took place between Mary and Joseph after the birth of Jesus, and that the “brothers” and “sisters” of Jesus one finds in the New Testament are the biological children of both Mary and Joseph, being Christ’s half-siblings. While this view (the “Helvidian” view, to give it its historical title) has never been officially proclaimed by the Church as the belief of the Church, it is the working position of all commentators and leaders of the Church (I only know of one LDS scholar, Jeffrey Chadwick, who believes the brothers/sisters of Jesus were children of Joseph from a previous marriage, though he rejects Mary being a perpetual virgin).
One text that, since the time of Augustine, has been cited in favour of this belief are the words of Mary to Gabriel, after finding out that she would be the mother of the Messiah:
Then said Mary unto the angel, how shall this be, seeing I know not a man? (Luke 1:34)
Augustine, in On Holy Virginity 4 wrote about this verse:
Her virginity also itself was on this account more pleasing and accepted, in that it was not that Christ being conceived in her, rescued it beforehand from a husband who would violate it, Himself to preserve it; but, before He was conceived, chose it, already dedicated to God, as that from which to be born. This is shown by the words which Mary spake in answer to the Angel announcing to her her conception; "How," saith she, "shall this be, seeing I know not a man?"
One online Catholic apologist provided a similar “take” on this passage vis-à-vis Mary being an avowed (perpetual) virgin:
Here comes when the incarnation is announced to Mary. Here is where Mary is told by the angel Gabriel that she will conceive and bear a child who is the Messiah who will reign. This is strange and wonderful news to Mary. We first note that the angel says to Mary, future tense, you will conceive in your womb. Mary is asking how this can be, since I know no man? Is this a pledge that she will remain a virgin even after she gets married to Joseph, as us Catholics would say? Modern Protestants will say, well ‘when she says I know no man’ she is only speaking about her present state, not speaking about any pledge for the future. Now, putting aside the technicalities, let us use a similar statement on another issue and see how we would understand a similar response.
Let us say someone comes to me and says ‘You will smoke a cigarette’, future tense. My response is ‘How can this be since I do not smoke?’ Technically my response is only in the present tense and not addressing the future. But the statement that I am addressing is dealing with that future. Thus, the statement I am making is not, ‘well, up to now I have not smoked, but I will smoke in the future.’ Because if that is the case, if I intend to smoke in the future, there is no reason for me to ask the question. When I say, albeit in a present tense, I do not smoke; my question is addressing a statement made about the future. Thus, when I say ‘I do not smoke’ it does not mean ‘I have not smoked in the past but I intend to smoke in the future.’ It means I have not smoked in the past, I do not smoke now, and I will not smoke in the future.
Much has been made out of the force of Mary's use of the present tense. However, as many grammarians (e.g.) show, the present tense may be used to emphasise that the results of a past action are still continuing. In this light, Mary's words are to be understood that at that point of time, she was still a virgin, but no hint whatsoever that she took a vow of virginity.
Daniel Wallace presents the following examples, alongside Luke 1:28, in the Greek New Testament in his book, Greek Grammar Beyond the Basics, pp.533 (emphasis added):
The way in which Paul introduces the quotation from Isa 53 implies that Isaiah’s words were still applicable to Paul’s situation. Typically quotations of the OT, other than prophecies, are introduced by γέγραπται, “It stands written.” It is difficult to assess the difference in force between these two introductory formulas, but it is possible that the connotation of the tenses is the following: (1) γέγραπται, being a perfect tense, stresses the abiding authority of scripture; (2) λέγει, being a present tense, stresses the applicability of scripture to the present situation.
Occasionally the NT writers do not name the subject of λέγει when introducing a quotation from the OT. A most probable explanation is that to them, what the scripture says is what God says and, consequently, there is no difference between scripture and God’s word. A significant text, in light of this discussion, is Eph 5:14. Although λέγει introduces the quotation, it is probably not from the OT. Rather, it may well be a quotation of an early Christian creedal hymn.
The perfective present is here joined by καί to a perfect tense, illustrating its force.
There are also other issues with the idea that Mary took a vow of perpetual virginity. For instance, the interpretation of Augustine et al. introduces a historical novum, namely the idea of a married virgin. We know from Luke 1:27 that Mary was betrothed/engaged to Joseph (cf. Matt 1:18).