Inbreeding

"Marvolo, his son, Morfin, and his daughter, Merope, were the last of the Gaunts, a very ancient wizarding family noted for a vein of instability and violence that flourished through the generations due to their habit of marrying their own cousins."

- Albus Dumbledore regarding inbreeding

Inbreeding with pure-bloods is a common practise for elite wizarding families wanting to uphold the tradition of marrying only wizards of respected ancestry. It is noted that wizarding families became more diverse as time passed as wizards began to marry half-bloods, Muggle-borns, and Muggles. Nevertheless, more conventional, elitist families tended to marry within their family, particularly cousins.

The Black family
The House of Black's family motto had always been "Toujours pur", which meant "Always Pure". Therefore, the family was strictly traditionalised to marry other 'noble' families (failing this, extremely rich families). The Black family took their motto seriously, and all family members who did not conform with the Black views of pure-blood supremacy were disowned quickly (i.e. Sirius Black). Squibs were also disowned.

In desperation to keep with the tradition, the Blacks resorted to extremes. Orion and Walburga Black were second cousins, as both their grandparents were siblings, and married, eventually had two children together.

Due to the Black family tree tapestry large family tree of the Blacks, it is possible that related people marry or interact, not knowing of their relationship.

The Gaunt family
The House of Gaunt had a fanatical belief in blood-purity, stemming from their esteemed ancestors Salazar Slytherin and Cadmus Peverell. To maintain their heritage's purity, they tend to marry their own cousins, which also allows them to pass down Slytherin's Parseltongue ability. This led to the members of the family to deteriorate mentally and physiologically, and they squandered much of their family gold long before the 1950s. As such, Marvolo Gaunt and his son Morfin suffered much mental instability, accompanied with violence, and disproportionate bodily appearances.

Other families
The Lestrange family is noted to be one of the few fanatical families who are willing to practise inbreeding to maintain purity.

The Weasley family, despite being pro-Muggle and unwilling to take up inbreeding for the sake of purity, does have certain signs of having engaged in it. Arthur and Molly Weasley are possibly second cousins once removed. Further, their granddaughter Victoire is in a relationship with her fourth cousin once removed, Teddy Lupin. However, these relationships are merely coincidental, and are out of genuine love as opposed to fanatical familial obligations.

Side effects of inbreeding
In Muggle genetics studies, it is proven that inbreeding can lead to serious problems, even for wizards. Notable effects that are seen in families are infertility (which would explain the extinction of the Black family) and disorders, both mental, emotional and physical. It is evident in many families (e.g. the House of Gaunt and notably insane Death Eaters of the Black family) that insanity is a common resultant. During Harry Potter's time at Hogwarts, he notes how the Slytherins seem 'an ugly bunch'. This could be explained by a lack of genetic diversity in the pure-blooded families Slytherin House favours. Because of the implications of inbreeding, the families claiming to be pure are declining.

Wizarding views
"Most wizards these days are half-blood anyway. If we hadn't married Muggles we'd've died out."

- Ron Weasley regarding the wizarding population

Due to the dangers of inbreeding, many wizarding families eschews such practises, particularly the Muggle-admiring family the Weasleys. By Hermione Granger's claim, there are not enough pure-bloods to compose the entire Death Eaters organisation, and that they are more likely half-bloods clinging onto their wizarding ancestries, pretending to be pure, furthering the rejection of inbreeding, even among the fanatics. Severus Snape, Dolores Umbridge and even Lord Voldemort are such examples.

"The family has, however, eschewed the somewhat dangerous practise of inter-marrying within such a small pool of pure-bloods that they become enfeebled or unstable, unlike a small minority of fanatic families such as the Gaunts and Lestranges, and many a half-blood appears on the Malfoy family tree."

- Description of the Malfoy family

The Malfoy family has been inclined to blood-purity since ancient times, though even they would not be willing to intermarry with cousins, believing the practise would endanger them, instead be willing to marry half-bloods. This differs them from the small minority families of the true fanatics such as the Gaunts, Blacks, and Lestranges.