Cousin marriage is in some societies allowed with one side of your family but not the other (the mother's side, but not the father's - the father's side but not the mother's) Cousin marrige is not uncommon within traditional societies around the world. If the culture is patriarchal, then your aunts/uncles on your father's side are much like mothers/fathers. Their children are much like sisters/brothers. AND therefore you would not marry in your father's line. But, if the culture is matriarchal, the exact reverse is true. Aunts/uncles on your mothers side are much like your mother/father. Their children are like sisters/brothers. And therefore you would not marry in your mother's line.
Incest is defined culturally not medically. Within the US today each state decides how close sanguinaly, or by blood, marriage partners can be. Con-sanguinal cousins might be the children of aunts and uncles and therefore off-limits, or some other rule will be applied depending on the state.
Also marriage between cousins is not as dangerous as people think. That too is part of the lore of culture. Over time cousin marriage has built up into something DANGEROUS. The original reasons for incest taboos had nothing to do with genetics or sex. These began a cultural rules that defined who a man and a woman might marry in order to know which family their children would belong to -- so that the inheritance of property, animals, wealth would not become confused and lead to conflicts.
From a very funny article about cousin marriage in Britain:
“The bottom line is that unless you know there is a genetic defect in the family there’s no reason why you shouldn’t marry your cousin.
“Any two people randomly have, roughly, a two per cent chance of having a child that has some kind of genetic abnormality. If first cousins marry then it’s roughly four per cent. So one side says ‘that’s doubling the risk’ while the other says ’96 per cent of people aren’t having a problem’. You can look at it both ways,” she says.
ANU News Kissing cousins: Studying historic inbreeding in rural English villages
And now a serious article from a legal news source, FindLaw
A panoply of state laws say cousin marriages are taboo. But a new report in the Journal of Genetic Counseling, described in the New York Times last week, might send state lawmakers back to work revising their incest laws.
The report concludes that cousins can have children together without running much greater risk than a "normal" couple of their children having genetic abnormalities. Accordingly, the report potentially undermines the primary justification for laws that prevent first cousins from marrying or engaging in sexual relations with one another.
...
According to the recent report, children of unrelated parents have a 3 percent to 4 percent chance of being born with a serious birth defect. Children of first cousins have only a slighter higher risk--roughly a 4 percent to 7 percent chance. Thus, the ban on cousin marriages will not go very far toward the general problem of preventing birth defects. CNN.com - FindLaw Forum: A genetic report should cause a rethinking of incest laws - April 9, 2002