Consanguinity
Consanguinity ("con- (with) sanguine (blood) -ity") refers to the property of being from the same genetic lineage as another person.  In that respect, consanguinity is the quality of being descended from the same ancestor as another person. Consanguinity is an important legal concept in that the laws of many jurisdictions consider consanguinity as a factor in deciding whether two individuals may be married or whether a given person receives property when a deceased person does not leave a will.
The degree of relative consanguinity can be illustrated with a consanguinity table, in which each level of lineal consanguinity (i.e., generation) appears as a row, and individuals with a collaterally-consanguineous relationship share the same row. See, e.g., table of consanguinity.

# Genetic definition
As a working definition, unions contracted between persons biologically related as second cousins or closer (F  0.0156) are categorized as consanguineous. This arbitrary limit has been chosen because the genetic influence in marriages between couples related to a lesser degree would usually be expected to differ only slightly from that observed in the general population. Globally, the most common form of consanguineous union contracted is between first cousins, in which the spouses share 1/8 of their genes inherited from a common ancestor, and so their progeny are homozygous (or more correctly autozygous) at 1/16 of all loci. Conventionally this is expressed as the coefficient of inbreeding (F) and for first cousin offspring,F = 0.0625. That is, the progeny are predicted to have inherited identical gene copies from each parent at 6.25% of all gene loci, over and above the baseline level of homozygosity in the general population. In some large human populations genetically closer marriages also are favoured, in particular uncle-niece and double first cousin unions where the level of homozygosity in the progeny is equivalent to = 0.125.

# Legal definitions
In regard to family law, generally, consanguinity becomes important in defining who may marry.  Some states, e.g., forbid cousins to marry.  Others are more lenient and forbid only brothers, sisters, mothers, fathers, or aunts and uncles to marry.  On a related note, many states prevent individuals from serving on a jury in which they have a certain degree of consanguinity with the defendant.
In regard to the law of intestate succession (when a person dies without a will), under the Uniform Probate Code section 2-103, after a surviving spouse receives his or her share, the descendants (depending on the circumstances this may include children, grandchildren, or great grandchildren either biological or adopted) receive the remainder of the intestate estate.  If there are no children, the decedent's parent(s) receive the remainder of the estate.  If there are neither descendants nor parents, the decedent's estate is distributed to descendants of the decedent's parents (again, depending on the circumstances, brothers and sisters, nieces and nephews, grand nieces and nephews and great grand nieces and nephews).  If there are no descendants, parents, or descendants of parents, then the deceased's property passes to descendants of the grandparents of the decedent (uncles and aunts, first cousins, or first cousins once, twice, or thrice removed).  Interactive programs showing the distribution of intestate property according to the laws of the different American states are found at MyStateWill.com, which also includes a useful Degrees of Kinship Chart
The connotations of degree of consanguinity varies by context (e.g., Canon law, Roman law, etc.). Most cultures define a degree of consanguinity below which sexual interrelationships are regarded as incestuous (the "prohibited degree of kinship"). 
In the Roman Catholic Church, unwittingly marrying a closely-consanguineous blood relative is grounds for an annulment, but dispensations were granted, actually almost routinely (the Catholic Church's ban on marriage within the fourth degree of relationship (first cousins) lasted from 1550 to 1917; before that, the prohibition was to marriages between as much as seventh degree of kinship).
Adoption may or may not be considered at law to create such a bond; in most Western societies, adoptive relationships are considered blood relationships for these purposes, but in others, including both Japan and ancient Rome, it was common for a couple with only daughters to adopt a son-in-law, making the marriage one between adoptive siblings.
Among the Christian Habesha highlanders of Ethiopia and Eritrea (the predominantly orthodox Christian Amhara and Tigray-Tigrinya), it is a tradition to be able to recount one's paternal ancestors at least 7 generations away starting from early childhood, because "those with a common patrilineal ancestor less than seven generations away are considered 'brother and sister' and may not marry." The rule is less strict on the mother's side, where the limit is about four generations back, but still determined patrilinearly. This rule does not apply to Muslims or other ethnic groups.

# Rates of occurrence
Historically, some European nobles cited a close degree of consanguinity when they required convenient grounds for divorce, especially in contexts where religious doctrine forbade the voluntary dissolution of an unhappy or childless marriage. Conversely, the consanguinity law of succession requires the next monarch to be of the same blood of the previous one; allowing, for example, illegitimate children to inherit.
- International Centre for Genetic Engineering and Biotechnology It is estimated that 55% of marriages between Muslims in the United Kingdom (and much of the Muslim world in general) are between first cousins, where "preferential patrilateral parallel cousin marriage" (where a boy marries his father's brother's daughter) is often favored.