Which Roman Catholic doctrines are infallible? I know that the Pope can speak infallibly (ex cathedra), and that this has officially been done once, as well as three times before Papal infallibility was formally declared. I would assume that any doctrine he talks about or mentions would be infallible, at least with regards to the bits spoken while in ex cathedra mode. Additionally, however, I can't immediately think of a reason why ex cathedra statements would be the only ones to result in infallible doctrines. Thus, my question is: which doctrines of the Roman Catholic church are infallible?

If none, many, or all of Roman Catholic Church doctrines are infallible, then say so. In the case of many, a broad classification would be appreciated. If there is a small number of them, then a list would be greatly appreciated.
Short answer: According to the catholic church, ALL of its doctrines are infallible.

Long answer:
The problem arises when someone questions whether a particular subject (matter of grave importance) is a Catholic doctrine or not. When that occurs, and there is an eminent danger of those people (who may or may not hold an ecclesiastical post) present a false doctrine as official church teaching, then pope has to step in and clear the matter by pronouncing a doctrine as a dogma. Now, there are some doctrines which will never be formally defined as dogmas, probably because no one will question them. (for example, virgin birth of Christ)

I understand that there is a room to wiggle around with respect to a doctrine. But as with a dogma, it is, with no second thought, infallible from a Catholic POV

Wikipedia article on Papal infallibility lists out seven instances of a pope speaking ex cathedra:


  
  "Tome to Flavian", Pope Leo I, 449, on the two natures in Christ, received by the Council of Chalcedon;
  Letter of Pope Agatho, 680, on the two wills of Christ, received by the Third Council of Constantinople;
  Benedictus Deus, Pope Benedict XII, 1336, on the beatific vision of the just after death rather than only just prior to final judgment;
  Cum occasione, Pope Innocent X, 1653, condemning five propositions of Jansen as heretical;
  Auctorem fidei, Pope Pius VI, 1794, condemning seven Jansenist propositions of the Synod of Pistoia as heretical;
  Ineffabilis Deus, Pope Pius IX, 1854, defining the Immaculate Conception;
  Munificentissimus Deus, Pope Pius XII, 1950, defining the Assumption of Mary.
  


The above article also states that there is no complete list of doctrines or dogmas ever prepared by the Holy See. Which understandably is an impossible task.

My personal opinion: When ever a canonization occurs, it is infallible too, because it satisfies all of the criteria of an infallible statement.

Just a footnote: A dogma is a doctrine to be believed by Catholics that has been proposed by the Church to be divinely and formally revealed. A dogma can be defined by a valid ecumenical council, approved by the pope. Or by the pope himself alone. Doctrine just means teaching which are assumed to be accepted by the universal church. There is no formal declaration is needed for a doctrine. Always a dogma and a doctrine will not contradict the scriptures.