As rumored (accurately this time), the SSPX excommunications were lifted.
The decree is translated here, at NLM.
Let’s look at what exactly this means, for those not familiar with the ins and outs of these things.
This is a very specific act.
In 1988, Archbishop Lefebvre, the founder of the SSPX, consecrated 4 bishops, despite being warned not to do so by Rome. The four bishops were excommunicated by name as well as Lefebvre and Bishop Antônio de Castro Mayer, who assisted.
What happened today is that those excommunications of those four bishops were lifted.
It doesn’t mean that the complexities of the SSPX situation are cleared up.  It is important to note that these figures, as priests and bishops, are still suspended. The canonical questions of suspension, jurisdiction and so, are knotty. Note that the question has never been of SSPX Masses being “invalid.” It is of priests’ jurisdiction to do things like say Mass, hear confessions and witness marriages, which is a different issue. We have canonists among us, who can perhaps explain.
This blog does a good job:

However, that does not mean that all is well with these bishops and the clergy of the SSPX. Whilst no longer excommunicated, these bishops are still not proper Catholic bishops in union with Rome. They lack the necessary permission to act as bishops, and the priests who work under them do not have the necessary permissions to act as priests. The division between the SSPX and Rome has not been healed, and it is still a very serious matter for a Catholic to receive the sacraments from a member of the SSPX in all but emergency situations. SSPX clergy do not have the necessary permission from Rome or from local bishops to carry out their work anywhere in the world. The Pope lifting the excommunications does not mean that the separation between the SSPX and Rome has ended. However, it is a move which seems to promise a sincere effort on Rome’s behalf to bring the SSPX back into the tent of the Church. The ball is now very much in the SSPX’s court in terms of how they will respond to this gesture.
It should especially be noted that the lifting of the excommunication does not mean that the Pope agrees with anything or everything that the SSPX bishops might say. In a singularly infelicitous episode, one of the SSPX bishops seems to have denied the holocaust recently. Do not let anyone try and convince you that the Pope endorses these views. Sometimes it is necessary to extend mercy to people whom we do not approve of – in this case, for the sake of the souls of the SSPX clergy and the people who attend their chapels, the Pope has been very brave in persisting with this act of mercy even though it threatens to be a PR disaster.

I am not one to read the Holy Father’s mind, but here is my long-distant assessment of this:
The Pope is not stupid. He knows the ins and outs of the SSPX better than any of us and is deeply familiar with the various currents of belief, practice and attitude that run through it. There are virulent anti-Semites in the SSPX. There are near-sedevacantists . There are many who believe that the Second Vatican Council was an illegitimate, invalid council. There are those who believe that the Mass that most of reading this blog go to every Sunday, if not every day, is invalid and that the elements are not consecrated.
But he also knows, particularly in Europe, there are many SSPX adherents who do not share these views and are simply seeking to practice a richer Catholic faith than is available to them in their local regular parish. I think to really understand the whole picture on this, you have to understand the European situation, which in many ways is quite different than it is here.
I think what the Pope knows is that there is going to be a huge degree of self-selection going on over the next few years, as well as some inevitably self-destructive behavior. In short, those who truly want to be union with Rome will do so, and the holdouts will hold out until some fantasy moment occurs in which the Novus Ordo Mass and the Second Vatican Council is repudiated.
It is not a stretch to see that this will actually lead to some division within the SSPX itself, even dramatic division among the leadership.
Zadok:

Personally, I think that this is a very generous act of the Holy Father, and I hope that no one would doubt his good will and sincerity. It will attract criticism, no doubt, but it’s important to understand precisely what this gesture means. It’s a gesture of mercy because the excommunications were justly imposed. It’s a concrete sign that the Holy Father wants to bring the Society back into communion. However, my understanding of this (and I admit that I’m not a canonist) is that this is simply a starting point. Bishops Fellay et al still lack jurisdiction within the Church and the Society cannot be said to have been restored into full communion. Bishops Fellay and the clergy of the society are still canonically irregular and do not have faculties to exercise their ministry. Whilst not excommunicate because of their irregular consecration, the Bishops of the Society are not properly members of the Catholic Hierarchy. Membership of the College of Bishops depends, not only on valid episcopal consecration, but also on hierarchal communion with the Bishop of Rome and the other Bishops.
It should also be noted that there is a lot of theological ground which needs to be covered, especially in the area of religious liberty, the authority of the Second Vatican Council and the newer liturgy. The clergy of the SSPX will need to undergo a severe examination of conscience regarding some of the things they have said over the past few years. However, with charity and the work of the Holy Spirit, wounds can be healed.

Fr. Tim Finigan (from England):

Some reactions are beginning to come in. Cardinal Vingt-Trois, Archbishop of Paris, in an interview this morning with Radio Notre Dame expressed some cautionary remarks but said:
I am delighted. This is an opportunity, a door open to allow Christians to find the fullness of communion with the Church. As long as they want or they accept it. It is a gesture of mercy and a gesture of openness to strengthen the unity of the Church.
The Chairman of the German Conference of Bishops has issued a statement in which he says that the Pope has offered his outstretched hand and that he hopes that they take it.
Not everyone is happy, of course: I am not thinking of the sandalistas or the secularists but of many good and sound Catholics who are concerned at the tendencies shown by some within the SSPX and given voice especially by Bishop Williamson. Damian Thompson has written a good piece this morning which summarises those concerns. (See: Pope Benedict is taking a huge risk in lifting the SSPX excommunications). I agree that he is taking a huge risk and that “Joseph Ratzinger has already factored the hostile reaction into the equation.”
As I indicated yesterday, I am delighted by this news. I have met some very good people from the SSPX and it is a great joy to know that the principal obstruction to their full jurisdictional normality in the Church has now been removed. It is a typically “Benedictine” move to have the announcement made during the Octave of Prayer for Christian Unity and I trust Pope Benedict’s judgement that this will “promote unity in the charity of the universal Church.” Nevertheless, Damian is right to say that “This is the biggest risk that Pope Benedict has taken in his pontificate so far.”

I would like to point out that the French Cardinal’s response is very telling.  France is one of the main flash points for the SSPX – the urban myth (I don’t know if it’s true) is that on any given Sunday, more French Catholics attend SSPX Masses than Masses in regular parishes in communion with Rome. The French clergy and hierarchy have been very hostile to the SSPX (and the feeling has been mutual). I think that if Vingt-Trois can respond in this way, that says something, especially about groundwork that has been in work behind the scenes.
Damian Thompson will be all over this on his Holy Smoke blog, and the comments there will be interesting, too.
I am going to lift a very helpful comment from a thread at the New Liturgical Movement. It is clarifying:

After having carefully read the decree and the responses, I’d like to make the following initial observations:
1) The decree simply lifts the censure of excommunication and deprives it of any effect as of January 21, 2009. There is silence on whether the original decree of excommunication imposed on July 1, 1988 was valid, and the decree seems to imply that yes, it was. Take note that the decree neither declares the excommunications null and void from the beginning, nor does it mention any posthumous rehabilitation of Archbishop Marcel Lefebvre and Bishop Antonio de Castro Mayer. Thus, the Pope has struck a middle course: lift the excommunications as desired by the SSPX, without declaring the excommunications to have been invalid from the beginning.

Had Pope Benedict XVI declared the excommunications invalid from the beginning, that would have been seen as a massive slap to the face of the late Pope John Paul II. Of course, he did not do that. I don’t think he could have been expected to do that in the first place, whatever his actual opinions on the matter may have been.
2) The decree mentions that the Pope did this out of his “paternal sensitivity” to the pain suffered by the four bishops because of the excommunications, out of his desire for unity among the faithul, and in the hope that by thus lifting the burden of excommunication from the four bishops, the SSPX will be moved to reconcile with the Holy See. It is clear that the Pope is now extending the utmost mercy and clemency to the SSPX; I hope that the world’s bishops will take note and follow suit. At the same time, I pray that the SSPX’s hardliners will not abuse the Pope’s amazing generosity.
3) The lifting of the excommunications on the SSPX bishops does not signify that the SSPX is back in full communion with the Holy See. This is clear from the wording of the decree:
“It is hoped that this step be followed by the prompt accomplishment of full communion with the Church of the entire Fraternity of Saint Pius X, thus testifying true fidelity and true recognition of the Magisterium and of the authority of the Pope with the proof of visible unity.”
Basically, what the Pope is saying is: “Ok, SSPX bishops, I’ve removed your excommunications. It is now up to you to reconcile with the the Church”. It will be interesting to see what the SSPX will now do. The ball is in their court now. So, the SSPX bishops are NOT YET bishops in good standing; but they are now Catholic bishops, that is for sure.
All these seem to imply that the suspension a divinis remains for all SSPX priests and bishops.
4) Interestingly, the Holy See is referring to:
“..trusting in the effort expressed by them in the aforementioned letter of not sparing any effort to deepen the necessary discussions with the Authority of the Holy See in the still open matters, so as to achieve shortly a full and satisfactory solution of the problem posed in the origin…”
This signifies that the Holy See is now willing to open talks with the SSPX to resolve the SSPX’s difficulties with Vatican II, provided that these discussions will touch only on “still open matters.” This refers to the SSPX’s demand for “dialogue” on doctrinal matters with Rome.
The SSPX has always made clear that it will not reconcile with Rome unless Rome rejects Vatican II’s “errors and ambiguities” . However, in the SSPX’s response to this decree, Bishop Bernard Fellay has considerably toned down his position, simply stating that the SSPX has “some reservations” on Vatican II. I find this to be very hopeful.

Canonist Ed Peters weighs in with some early thoughts:

Based on what is public so far (in what are obviously only quick translations), it seems that Pope Benedict sees something like the “withdrawal from contumacy” required by 1983 CIC 1358 for the lifting of censures Light of the Law, 3 feb. 2006). That would be cause for rejoicing, to be sure, healing another wound on the mystical Body of Christ. Having said that, however, I confess that I’m having a hard time seeing in Bp. Bernard Fellay’s January 24th letter to the faithful, at least, any withdrawal from contumacy for the actual canonical crimes he and the others committed (receiving episcopal orders without pontifical mandate, ), or for that matter, much of a retreat from anything else he has said for the last 20+ years.

Fr. Z has a very good Q & A, as well.

Q: Is it okay for the SSPX bishops to ordain now?
No. The bishops of the SSPX are validly consecrated bishops, but the fact remains that they were illicitly consecrated.  That hasn’t changed.  They are still not reconciled with the Bishop of Rome.  They are still suspended a divinis.  They still have no permission to exercise ministry in the Church.  They may not licitly ordain.  They have no authority to establish parishes, etc.
Q: Are the chapels of the SSPX okay now?
Not in a juridical, legal sense, no.  Many good things can happen in one of those communities, but the SSPX chapels are not, because of the lifting of the excommunications, suddenly made legitimate.  They are not reconciled by this move.
Q: Are the priests of the SSPX in good standing now?
Not yet they aren’t.  The priests of the SSPX are still suspended a divinis.  They say Mass vaildly, but without the permission of the Church, either from a faculty of the Holy See or the local bishop.  They do not have the necessary faculties to hear confessions and give sacramental absolution except in danger of death.