Hereditary Curse

However, the giants of the Sul’at League studied the Gyrderi and found a way to counter the druids—the giants enacted a terrible curse that forever bound them in the wild shapes they were wearing, trapping them and their descendants in the forms of animals.

—Eberron Secrets of Xen'drik, Chapter 3

A Hereditary Curse is particular type of supernatural Curse, that is passed from parent to offspring, usually until the entire family line(s) die out (and the curse with it) or unless they find some way to break the curse.

Usually, it was specifically placed upon the family by someone else, but sometimes it can be the result of Karma received or Black Magic performed by an originating family member. In some cases, it can even be the price paid for making a particular vow.

The existence of a Hereditary Curse usually makes breaking the curse one of the primary motivators for a character carrying that curse. Sometimes the way to find break the curse is already known; other times the character must discover it for themselves. Often the character that appears in a work of fiction with the curse is the last surviving member of their family, and therefore the only one that has any hope of breaking the curse. This need not always be the case, however.

Not to be confused with In the Blood, which is when there is a fear that having evil ancestors might make you evil; It Runs in The Family, which describes a family of eccentric and sometimes crazy relatives; and Sins of Our Fathers, which involves any example of character or group taking revenge on a long dead person's descendants.

A Sub-Trope of Curse. If a curse turns one into a monster, than the first ancestor to suffer it is the Monster Progenitor. If the curse cause one to die early, it can be a case of Your Days Are Numbered.

Examples of Hereditary Curse include:

Anime and Manga

In Inuyasha, Miroku's family was cursed by Naraku with the Wind Tunnel: a black hole in the palm of the right hand that's passed down through each generation. The Wind Tunnel absorbs everything in front of it unless sealed by enchanted prayer beads, and it's constantly expanding which culminates in it being strong enough to break the seal and consume its bearer and all that surrounds him, just like it has already done with Miroku's father and grandfather. The only way for Miroku to free himself and his descendants from this fate is to kill Naraku.
The Niwa and Hikari families in D.N.Angel each have a hereditary curse created by what essentially amounts to an magical accident. The Hikari seems to have gotten the worst of it, as their curse creates a Super-Powered Evil Side who tends to act without much regard to his "host", causing members of the Hikari family to all die young.
Fruits Basket has the Sohma family, which is under a curse that changes some members of the family into animals of the Eastern Zodiac when they are hugged by someone of the opposite sex that is not also subject to the curse. It's later revealed that there's another part to the curse: each cursed member finds it impossible to act in any way that isn't subservient to the family member cursed to be the reincarnation of the God of the Zodiac when in their presence.

Film

In Van Helsing the Valerious family is bound by a curse that keeps them from entering into Heaven until Dracula is killed. This is the result of a vow taken by a distant ancestor.
Penelope has the titular Penelope receive a hundred plus year old curse on her family that their first born daughter would be ugly until she were accepted by "one of her own." This is why her parents went about trying to get her married, but it turns out the curse can be interpreted as "when she accepts herself." As soon as she becomes okay with the idea that she's going to be ugly forever, and it's not a cause for angst, does the curse lift.
The curse of the Haddocks in Tintin. Red Rackham curses Sir Francis Haddock with his last breaths, vowing to meet him again in another life. The following generations of the Haddock family are plagued with bad luck until their last two descendants - Captain Haddock and the villain of the movie - fight it out.
Teen Wolfs werewolfism is passed down from parent to child. It totally freaks him out because he had no idea; his father didn't tell him because sometimes it skips a generation.
In Practical Magic, all the witches in the family are cursed in that any man they fall in love with is doomed to die an untimely death.

Literature

The Dresden Files has a Harley MacFinn in The Fool Moon, whose family curse originated from St. Patrick himself. They are all curse to become Loup-Garou (super-Werewolves) during the full moon.
The Avatar Trilogy has Kelemvor Lyonsbane, last scion of a family of cursed mercenaries. The curse began when his ancestor betrayed a powerful sorceress and was cursed to never again act purely for profit, or transform into a murderous panther. However, with the birth of his son, the curse reacted to the boys innocence and reversed itself. From then on, Lyonsanes could ONLY act on anothers behalf out of thoughts of profit.
In Harry Potter and the Deathly Hallows, Lupin is overcome with guilt when his wife becomes pregnant because he's worried that his lyncanthropy might be this.
The plot of Holes is driven by a bad luck curse on the main character's family due to an ancestor cheating a gypsy.
In Labyrinths of Echo, the descendants of the Moon Bulls clan are cursed to turn into Extreme Doormats during full moon.
In Tales of the Frog Princess: Once Upon a Curse, Princess Emma goes back in time in a desperate attempt to break the curse that haunts the females in her family: After they turn sixteen, if they come into contact with a flower, they turn into disagreeable, argumentative, unlovable hags.

Live-Action TV

In Jack and The Beanstalk: The Real Story, Jack's family suffers from a curse that kills the sons after exactly 40 years, which is ultimately the result of the original Jack's mother killing the giant, and being cursed to forever watch her descendants die young.

Religion and Mythology

In Greek Mythology, Tantalus prepared his own son Pelops as food for the gods. Not only was he himself punished for this gruesome act (but this is another story...) but also a curse was laid upon the next four generations of his house. How did this curse manifest itself? Let's just say that the House of Atreus (named after Tantalus' grandkid) took being a Dysfunctional Family Up to Eleven.
Several examples from The Bible.

Tabletop Game

Some of the noble families in the Ravenloft setting are saddled with these, such as the propensity to madness displayed by the Hiregaard clan in Legacies of the Blood. One of the most powerful spells introduced as part of the setting allows the caster to inflict this trope upon an enemy and their descendents.
Mage: The Awakening has the Proximi, magical legacies who have the somewhat limited ability to learn Awakened magic. The downside to this is that each line has its own curse, such as poverty, death at 45, etc. And don't even think about pursuing a Curse Escape Clause - if the curse is broken, then it just rewrites itself into a stricter format.

Video Games

In Oblivion's expansion pack Knights of the Nine, there is a man named Kellen in the Chapel of Stendarr who was cursed by something stupid his ancestor did. He's bedridden and can hardly stand from the fatigue caused by the curse. The player is supposed to cure him.
In The King of Fighters, thanks to a blood pact with Orochi, the Yagami clan (formerly the Yasakani) gained more powerful flames--but not without a price. Each heir dies young, while the mother dies during childbirth. In addition, since the clan now has Orochi's blood, this makes them all susceptible to the Riot of the Blood. Iori (the current heir) actually has no care in the world for his family's stigma, although there are hints that Iori is the one destined to finally break the curse.

Web Comics

On The Order of the Stick Eugene Greenhilt made a vow that neither him nor his descendants would be able to go into heaven until the Muderer of his Master (Xykon) was destroyed, however is it paritially suberted when the Celestial Bureaucracy allowed his son Roy to enter the Celestial Realm because he had died attempting to fulfill the Oath to the best of his abilities (including his ability to judge what was appropriate), whereas Eugene had consciously given up on it many years before and never once made one last attempt to defeat Xykon, preferring to hand responsibility off to his children instead.
In Achewood, both Pat and his father magically became homosexual due to the curse of Gladdington castle, wherein an ancestor of theirs was cursed such that all of his sons and their sons thereafter would become homosexual at the age of 26.

Web Original

Techwolf of the Whateley Universe. An amiable gadgeteer genius who, due to a witch's curse on one of his ancestors, looks like a seven foot tall werewolf all the time.