The Catholic Church only ordains men to the priesthood, something that is often questioned given that the Church of England and other bodies do. For example, the November 2012 debate in the Church of England synod about whether to ordain women as bishops reawakened interest in the issue. It's thus relevant to remember some of the reasons that the Catholic Church gives for not ordaining women. The teaching that the Church can only ordain men to the priesthood was infallibly taught by Pope John Paul II in 1994 and more recently reiterated by Pope Francis.
In summary, the Church teaches that:
Christ chose only men as His 12 Apostles the first priests. He made this choice freely despite the fact that many other things He did were contrary to the opinions and traditions of His time. The Church follows His example in continuing to only ordain men because we are His Church and do what He taught us. This position has been consistently upheld by the Tradition for all of the 2000 years of the Church and repeatedly confirmed by variously definitions of the Church, leading up to the infallible pronouncement by Pope St John Paul II in 1994.
In addition, theologians offer a number of different arguments as to why it is appropriate to ordain only men to the priesthood. Primary among these arguments is the notion that the priest stands as a particular 'image' or 'icon' of Christ and that having a priest of the same gender as Christ helps a manifest this. This notion was cited by Pope Francis when he reaffirmed the teaching on this point in 2013, saying, "The reservation of the priesthood to males, as a sign of Christ the Spouse who gives himself in the Eucharist, is not a question open to discussion"(Evangelii Gaudium n.104).
Finally, it's worth noting that the Anglican Communion does not share our Catholic understanding of what a priest is, what the Mass is, or our understanding of the Magisterium's role in transmitting and interpreting Christ's teaching on this and other issues for us. It's thus, sadly, not surprising that Anglicans and Catholics have come to a different conclusion on this matter.
Many of the best articles written on this subject were written shortly after the 1994 decree of Pope St John Paul II. Here are links to a few of the briefer articles:
Why Women Can't Be Priests by Mary DeTurris
DeTurris' article summarises the views of Sister Sara Butler. Sr Sara is well-known for the fact that she used to believe in women's ordination but changed her mind and now argues for the Church's teaching on this matter.
The All Male Priesthood by Fr William Saunders
Fr Saunders' article both argues from tradition and explains why this tradition makes sense.
Women Priests? by Fr William Most
A YouTube talk by the Papal Theologian Fr Wojciech Giertych
Is Ordinatio Sacerdotalis Infallible? by Paul Likoudis
This article argues, contrary to some dissenters, that the teaching by Pope St John Paul II on this point is infallible. This argument was formally clarified by the Vatican itself on 18 Nov 1995 when the Congregation for the Doctrine of the Faith decreed that this pronouncement "requires definitive assent...(and) has been set forth infallibly by the ordinary and universal Magisterium."