The Spanish Inquisition seems to have had plenty of support from the Universal Inquisition at the time, but what is the present Vatican's view? Has the Church repudiated the Inquisition?
Yes. The Catholic Church has repudiated the Spanish Inquisition. In fact the late Pope John Paul II has apologized for the atrocities committed during the Spanish inquisition.
In the Apostolic letter "TERTIO MILLENNIO ADVENIENTE" he made this apology:
Hence it is appropriate that as the second millennium of Christianity draws to a close the Church should become ever more fully conscious of the sinfulness of her children, recalling all those times in history when they departed from the spirit of Christ and His Gospel and, instead of offering to the world the witness of a life inspired by the values of her faith, indulged in ways of thinking and acting which were truly forms of counter-witness and scandal. Although she is holy because of her incorporation into Christ, the Church does not tire of doing penance. Before God and man, she always acknowledges as her own her sinful sons and daughters.
He also reiterated his apology in his letter to Cardinal Roger Etchegaray on the occasion of the release of the "Report of the International Symposium on the Inquisition".
What is currently called the Congregation for the Doctrine of the Faith used to be called Congregation for Universal Inquisition (erected in 1542), which changed its name to Congregation of the Holy Office in 1908. The Spanish Inquisition was just the Spanish branch of the Inquisition.
Also, a good book on the Inquisition, which dispels the myth that the Catholic Church executed people (it was the State who actually did that), is canon lawyer Ed Peters's Inquisition. There's also a good Old Catholic Encyclopedia article "Inquisition."
Related to this is St. Thomas Aquinas's discussion of the question "Whether heretics ought to be tolerated?":
With regard to heretics two points must be observed: one, on their own side; the other, on the side of the Church. On their own side there is the sin, whereby they deserve not only to be separated from the Church by excommunication, but also to be severed from the world by death. For it is a much graver matter to corrupt the faith which quickens the soul, than to forge money, which supports temporal life. Wherefore if forgers of money and other evil-doers are forthwith condemned to death by the secular authority, much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death.
On the part of the Church, however, there is mercy which looks to the conversion of the wanderer, wherefore she condemns not at once, but "after the first and second admonition," as the Apostle directs: after that, if he is yet stubborn, the Church no longer hoping for his conversion, looks to the salvation of others, by excommunicating him and separating him from the Church, and furthermore delivers him to the secular tribunal to be exterminated thereby from the world by death. For Jerome commenting on Gal. 5:9, "A little leaven," says: "Cut off the decayed flesh, expel the mangy sheep from the fold, lest the whole house, the whole paste, the whole body, the whole flock, burn, perish, rot, die. Arius was but one spark in Alexandria, but as that spark was not at once put out, the whole earth was laid waste by its flame."