In pre-Christian Europe and most of the Non-Christian World today First Cousins not only were permitted to marry, were expected to marry each other. After the Fall of the Roman Empire in the West, the Catholic Church double the people on can NOT marry under Jewish and Roman Law. This expansion included First Cousins (i.e. for the first time in European History First cousins were NOT only not expected to marry but were FORBIDDEN to marry). The main reason for this was to break up the old Roman Aristocracy that controlled almost all of the lands of Europe even after the Empire had fallen and the Technical rulers were the Germanic tribes. This concentration of wealth in the form of land had been the chief problem within the Roman Republic and later Empire (In the Second century BC, the Gracchi tried to undo this concentration of land and were assassinated for it, furthermore the Roman Republic turned to a Mercenary Army, for the Militia Army that had Defeated Hannibal had supported the Gracchi and thus could no longer be trusted to keep existing property rights, which I should point out was illegal under Roman Law, but that law had been ignored since before Hannibal).
Thus even after the fall of the Roman Empire in the West, Roman aristocracy kept ownership of their lands. The adoption of the concept that you could NOT marry your cousin meant that the land would have to be divided among a larger group of people at the death of any land owner. As the Early Middle Ages (I refused to call them the "Dark Ages" for it was a time of improvements in the life of the poor, while the elites lost, money, land and power and since most of our information is from the elites it was a "Dark Age" for them, even while the peasants were slowly improving and would continue till improve till the Renaissance).
Now, since the 1800s, various rationales have appeared to justify the ban on Marring first cousins for some other reason then to make sure the wealth in NOT concentrated in the hands of just a few interrelated families. All of these rationales have failed, mostly because we, as a society, have NOT generally married our cousins for over 1500 years and most of the bad affects of such closing marrying have been minimized OR since first marrying is NOT the norm even, where legal, no inherited problems appear.
Just a comment WHY First Cousins were forbidden to marry. If no such ban had existed, we would be still marrying our cousins today (As does most of the "Non-Christian" World). We have run across one of the good points of such marriages in Iraq and Afghanistan. In those two countries, like much of the Moslem world, marrying first cousins in the norm. This has a side affect of strengthening families, tribes and clans over any wider organization. Thus in Iran and Afghanistan it has been hard to recruit people to spy on members of their own town, for most towns are organized on tribal basis and to spy is to turn traitor to not only your support group, but your spouses support group (Being cousins, both support group are almost the same). Anything that attacks that extended family/Clan/Tribe is an enemy of one and all members of that extended family/Clan/Tribe. Thus when we ended the War in Iraq we had to bribe the leadership of those extended family/Clan/Tribe NOT rely on a spy in the neighborhood to report to us what was going on. We can use such spys in Latin America for First Cousins rarely marry there and thus the support group is wider then one's extended family/Clan/Tribe just because one has relatives (and your spouse has relatives) that are outside the extended family/Clan/Tribe. This is one of the side affects of the ban on Cousin marrying, but what you lose in support from close relatives, you gain by having an wider extended family (But then you must accept the fact the wider support group is NOT as dedicated to you as would a interbreed extended family/Clan/Tribe as found in Iraq and most of the Non-Christian World.
Please note, I use the term "Christian" and "Non-Christian" to reflect the fact that it was the Early Middle Ages Christian Church that imposed this rule. It exist from Russia to Latin American do to the extent of the area where the Christian Church is or had been the dominate religion since the Early Middle Ages. Christianity is NOT the dominate force in those areas today, but traditions in those areas reflect Christian beliefs of the Middle Ages. Now, every Western Country, except the US, has legalized cousin marrying, but as noted above this was done AFTER the breakup of the old Roman elites (Around 900 AD) AND after most people in those Western Countries no longer looked at their first cousins as their first choice in mates (i.e. the problem caused by Cousin marrying, has either been long solved by the ban so the ban in no needed for most people do NOT look as their first cousins as their first choice of mates).
Please note China bans Cousins marrying for the same reason the Early Middle Ages Catholic Church did, to break up the concentration of wealth among certain groups, in the case of China Peasants who controlled certain parts of rural China.
The Gracchi:
http://en.wikipedia.org/wiki/GracchiSome more on first Cousins and Marriage:
http://en.wikipedia.org/wiki/Cousin_marriage