I don't have much to add to what Top Gun and Foil said, just a couple things...
As I understand things, the office of apostle is reserved for those personally called to teach and taught by Jesus himself. They spoke with great authority because their experience with Jesus was firsthand--if they faithfully represented his words and ideas, what they said was trustworthy. It's more than just having been an original witness to what Jesus said and did--it was being personally prepared by him to teach the gospel.
That limits it to his twelve disciples, with the exclusion of Judas (who was later replaced by Matthias), and Paul as well (whose firsthand experience with Jesus came in the form of visions). In fact, it's instructive to see how Paul defends his apostleship: See Acts 9 for Paul's conversion; see Galatians 1:11 - 2:21 for Paul's defense of his apostleship, emphasizing that his message is from Jesus himself, not learned from the other apostles; see as well 2 Corinthians 12:1-7 where Paul comments on various visions he has had.
Could Mary Magdalene have been another apostle? Strictly speaking, it's possible that she was personally taught and commanded to teach by Jesus--though scripture doesn't record that; it would be speculation. But if she
was prepared and commanded to be an apostle, she did a poor job of it: it wasn't exactly a private thing.
Having left so little in the way of legacy in the church, it's awfully unlikely.
There are gnostic texts that are supposed to contain secret messages given by Jesus to Mary Magdalene--at least, so Google tells me. I've never payed much attention to that. One of the essential elements of gnosticism was the idea of secret knowledge given only to the elite. Thus you have claims of a secret, more elite gospel whispered by Jesus to Thomas, which none of the other disciples were in on. That always strikes me as suspect, compared to the traditional gospels, which are both written by eyewitnesses and appeal to fellow witnesses at the time to confirm what Jesus said publicly. Moreover, reading those gnostic secret texts doesn't yield anything enlightening: the ones I have read are full of vacuous riddles, and not at all similar to the plain-spoken and profound style of Jesus.
There are scholars who really like the gnostic gospels, and suppose they present a more accurate picture of Jesus. If you believe Jesus was the sort of person who spoke in vacuous riddles, and all the beautiful and profound truths attributed to him were added later, I can see why the gnostics might appeal to you. But they really aren't very scholastically trustworthy, from what I've seen. (Based as they are on secret witnesses, changing as they do from century to century).
Probably the most laughable assertion of those who like the gnostic gospels are the occasional suggestions that certain truths were suppressed by the early church, and that's why we don't read them in the gospels. While I was googling for background on the idea of Mary Magdalene as an apostle, one of the sites I ran accross suggested that she had a foundational and extremely influential role in the early church, but that influence was suppressed and downplayed by the later patriarchal church. Such an idea might appeal to those familiar with the church of the middle ages--heavily patriarchal, tightly doctrinally controlled, etc. They're funny attributed to the church of the first century, though: extremely liberal in issues of gender, geographically widespread, constantly under persecution. The early church battled many heresies, and had neither the power to suppress them nor the authority to expunge them from history--could such a church really have convincingly rewritten its own history and utterly suppressed any knowledge of a widely influential founder?
There are those who think that it is evidence of their intelligence that they disagree with tradition. That's empty scholarly vanity. I think it accounts for a lot of odd academic theories about the origins of the church, the origins of the Bible, or the "real" historical Jesus. I think it's the same thing that drives some academics to support terrorism as ethical: the idea that disagreeing with the common knowledge is evidence that one is elite. I suppose I would (admittedly, cynically) put this down to that as well: it doesn't seem to me a theory that could withstand much scholarly skeptecism.
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On a tangent, Top Gun and Foil mentioned women's position in the church. It's sort of relevant to the topic here, because the church has historically had a hard time treating women fairly. That gives support to people who claim that a male-dominated church suppressed knowledge of female teachers and apostles. If that's true, it did a sloppy job of it: Jesus in the gospels goes out of his way to teach women with the same respect he teaches men, and Paul in the epistles often refers to women as fellow workers.
Women's role in the church is actually the subject of contemporary debate. On one side are the egalitarians, who argue that the church ought to make no distinction between women and men, and cite verses like Galatians 2:28--"There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus." I can't recall what the other side of the debate calls themselves, but they make any number of restrictions on womens' role in the church, citing such passages as 1 Timothy 2:11-12: "A woman should learn in quietness and full submission. I do not permit a woman to teach or to have authority over a man; she must be silent."
It's a curious and tangled debate these days, with different denominations and individual congregations taking different views of womens' role in the church. The church I grew up in only allowed male pastors and elders; the church Tom grew up in allowed married couples to serve as elders together. The church I grew up in allowed women to teach womens' adult classes and children's sunday school, but not adult mixed Sunday school (though I don't know if that was disallowed, or if no one ever asked...). Then again, I've taught adult Sunday School at the church I now attend, and nobody seems to mind.
One reflex outsiders have looking in on the debate is to suppose half of the church thinks women are worth less than men. That's entirely untrue of all but the most extreme positions: everyone agrees that women and man are of equal value as people, and before God. What the church is trying to do is simultaneously embrace the equality of men and women without the gender-blind equivalence the rest of the world endorses (and as well, it's trying to obey some rather difficult-to-understand commands). Everybody has good points and is arguing in good faith, and there are many varied positions to take on various stands of principle.
Orthodoxy these days seems to be that women shouldn't be pastors, and shouldn't be "the man" in a marriage. Just about everything else--from who women can teach to how they can serve administratively in the church--is up for debate. It's still an issue I'm working out for myself, so I can't say I can even give a fully formed opinion on the matter--though as someone who wants to teach, and has a lot to say to the church, it's certainly an issue close to my heart, and one I've given a lot of thought to.
[Edit: Discussing this with Tom, he pointed out that "orthodoxy" is too strong a term to describe the position that women shouldn't be pastors. As it stands, it's something that's debated in mainstream circles, but--to quote him--"nobody's really willing to push the line." That's probably more accurate... on that one, it's more a case of common consent and quiet debate than a matter of orthodoxy. However, the term "orthodoxy" is appropriate to describe the other position ("women shouldn't be 'the man' in a marriage"). ]