Here's the Catholic Encyclopedia article on consanguinity:

http://www.newadvent.org/cathen/04264a.htm

And one on affinity (i.e., deceased brother's wife, etc.):

http://www.newadvent.org/cathen/01178a.htm

Regarding consanguinity, here are a few highlights from the article (I have omitted citations to make it easier to read):

"Consanguinity is a diriment impediment of marriage as far as the fourth degree of kinship inclusive."

"[The] law of Theodosius . . . forbade (c. 384) the marriage of cousins. This law was retained in the Western Church, though it was revoked (400), at least in the East. . . . The Code of Justinian permitted the marriage of first cousins (consobrini), but the Greek Church in 692 condemned such marriages, and, according to Balsamon, even those of second cousins (sobrini).

"This discipline continued throughout the Church till the eighth century. . . [when] Gregory III (732) . . . forb[ade] marriage among the Germans to the seventh degree of consanguinity."

"While in the twelfth century the theory of the remote degrees was strictly maintained by canonists, councils, and popes, in practice marriages ignorantly contracted within them were healed by dispensation or dissimulation. Finally, in the Fourth Lateran Council (1215), Innocent III restricted consanguinity as a diriment impediment to the fourth degree. He explains that it was found difficult to carry out the extension to further degrees."

"Gregory I (590-604) . . .granted to the newly converted Anglo-Saxons restriction of the impediment to the fourth degree of consanguinity; Paul III restricted it to the second degree for American Indians, and also for natives of the Philippines. Benedict XIV (1757) states that the Roman pontiffs have never granted dispensation from the first degree of collateral consanguinity (brothers and sisters). For converted infidels it is recognized that the Church does not insist upon annulment of marriages beyond this first degree of consanguinity."

"Benedict XIV, as already said, emphasized the fact that the popes had never granted a dispensation for a marriage between brother and sister, even where the union might have occurred without a knowledge of the relationship on the part of the contracting persons."

"Even in the most conservative Catholic countries, there is a tendency to limit the impediment of consanguinity. In England the statutes of Henry VIII, repealed in part by Edward VI and wholly by Phillip and Mary, were revived in Elizabeth's first year, the provision being that "no prohibition, God's law except, shall trouble or impeach any marriage outside Levitical law". The ecclesiastical interpretation was that consanguinity was an impediment to marriage as far as the third degree of civil computation. A man might not marry his aunt, or his niece, but might marry his first cousin. Relationship by the half-blood was put on the same footing as the full-blood, and illegitimate consanguinity was treated as equivalent to legitimate blood relationship. The courts regarded marriages within the forbidden degree as voidable rather than void, but such marriages were declared void by an act of 5 and 6 William IV (1835). In the United States all the States prohibit marriage between lineal descendants; most of them prohibit marriages between uncle and niece, nephew and aunt, and between first cousins."