Generational Saga

This is a work that traces the evolution of a single family through multiple (usually three) generations, covering a long enough period of time that you get to see more than one generation at the same age or stage of life. Often it follows the pattern:
 * 1) The first-generation protagonist is an immigrant.
 * 2) The second-generation protagonist becomes entirely assimilated in the host culture.
 * 3) The third-generation protagonist ends up learning to appreciate their ancestral heritage.

With only two generations, the third-generation protagonist is usually the one omitted; works which follow this pattern through more than three generations might have multiple second-generation-type (assimilated) protagonists, or they might alternate between second- and third-generation-type protagonists.

Another frequent theme is that the first- and third-generation characters have more in common with each other than either does with the second-generation character. Often they both react in the same way to her, or (if the first-generation character is still alive when the third-generation character is around) form a bond that excludes her.

Note that properly speaking this only applies to unified works; having a sequel in which we meet Generation Xerox isn't enough. It's primarily a literary trope, though it also appears in theater and film; you might be able to see less-planned versions of it in long-running Soap Operas or possibly even Comic Books.

Compare An Immigrant's Tale.

Anime

 * JoJo's Bizarre Adventure.
 * Dragonball.
 * Kinnikuman and its sequel Kinnikuman Nisei.
 * Baccano
 * Mobile Suit Gundam Age.

Comic Books

 * Taking a leaf from the above description, if there was ever a comic continuity that became a Family Saga, it was Batman.
 * The entire DC Universe and Marvel Universe can be thought of as two great, big generational sagas (especially in regards to team titles like Teen Titans or Justice League of America for the former,and the many X Men or Avengers titles for the latter).
 * Also, Hulk comics. Interestingly, generation is a bit of a fluid thing here. The first generation is Bruce Banner, Jen Walters, and their supporting casts, then we get the second generation with Skaar and Lyra, the Hulk's son and daughter, as well as members of the first generation becoming Hulks themselves.
 * In the saga of The Metabarons, the entire history of the Metabarons is told from the start of the dynasty to the last Metabaron.

Film -- Live Action

 * The Godfather books/movies.
 * In Star Wars Episode III: Revenge of the Sith, Amidala states that this is how liberty dies, with thunderous applause. In A New Hope her daughter, Princess Leia, is acting as a spy for the Alliance to Restore the Republic (commonly known as the Rebel Alliance, and, informally, as the Rebellion) and in Return of the Jedi Leia tells Luke that she remembers her mother being very beautiful and kind but sad.
 * Legends of the Fall.
 * Bicentennial Man.
 * The movie American Pop covers four generations and their relationship to popular music in America
 * The movie Mi Familia, whose tagline is "Three generations of dreams."

Animated Films

 * In The Lion King Mufasa tells Simba that even when he's gone he'll always be there in the sky with the great kings to look down on his son. Once he is gone, Simba abandons the Pride Lands to his uncle Scar, but after talking to his father in the sky he realizes that he needs to come home and be king.

Literature

 * The definitive literary example is probably Thomas Mann's epic Buddenbrooks, which is also a Roman à Clef about his own family of North German merchants.
 * Middlesex by Jeffrey Eugenides follows this pattern for a family of Greek immigrants to the Detroit area.
 * Accelerando by Charles Stross; in this case, the "immigration" that occurs is into The Singularity.
 * Roots by Alex Haley is an extended example, going through seven generations.
 * One Hundred Years of Solitude by Gabriel Garcia Marquez.
 * The Joy Luck Club by Amy Tan. It only covers the first two generations of four sets of mothers and daughters, but they all follow the pattern.
 * The Edge Chronicles revolves primarily around generations of the Verginix family. Only two stories in the series aren't about members of the Verginix family; The Stone Pilot and The Blooding of Rufus Filatine.
 * John Jakes's Kent Family Chronicles, which covers 10 generations.
 * Song of Solomon by Toni Morrison has elements of this.
 * Older Than Print: This is the structure of various Icelandic sagas, which are the Trope Namers. Good examples are Laxdoela Saga, Eyrbyggja Saga, Grettir's Saga and Egil's Saga. These works all date from the 13th century.
 * The Love Comes Softly series by Janette Oke.
 * Both London and Sarum by Edward Rutherfurd trace a few families' non-consecutive generations from Stone Age England through to modern times. He's also done it for Russia (Russka) and Ireland (The Dublin Saga), among others.
 * This is pretty much James Michener's stock in trade.
 * Technically his novel Centennial covers residents going back essentially to the beginning of humanity, but the bulk of the narrative starts in the early nineteenth century. Such diverse characters as Mennonite farmers, French trappers, Arapaho natives, British nobility, and Scottish immigrants eventually combine into the main character set in the present day.
 * The Source covers the events at one (fictional) site in the Middle East from 10,000 BCE to 1962.
 * Hawaii and Alaska do this one better, the former going back to the creation of Hawaii via volcano over billions of years and the later going all the way back to the beginning of time.
 * For The Other Wiki's list of novels like this, see here.
 * Many early Danielle Steel novels fit this type, including Jewels.
 * Sidney Sheldon's Master of the Game follows four generations of one family in detail and also has appearances from an earlier and later one. The significant four generations are headed by, in order: A Scottish man who ventures to late-1800s South Africa to make his fortune in diamonds; his daughter, who devotes her life to making the resultant company even bigger and more powerful; her son, who wants to be an artist instead of her heir; and his Cain and Abel twin daughters. The first and second generations are similar, the third obviously different, and the twins split the difference -- one isn't interested in the company, the other most certainly is.
 * Harry Turtledove's two long-running series do this for two or three generations.
 * The Full Matilda discusses four generations of African-American servants living in Washington DC and their interactions with Matilda. The first generation is Matilda's father Jacob (only partially covered) becoming a servant during the early 20th century, the second generation discusses the Sibling Rivalry between Matilda and her brother when they start a catering company from The Roaring Twenties to The Fifties, the third generation is Martin's sons David and Rodrick (who starts a food distribution company) growing up in The Sixties, and the fourth is Rodrick's biracial son who is Desperately Looking for A Purpose In Life during the Turn of the Millennium.
 * Warrior Cats. The first series follows Fireheart as he joins the Clan and eventually becomes leader. The second series is from his children's point of view; they consider themselves Clanborn and don't really think much about their non-Clan roots. The third and fourth series are from his grandchildren's point of view, and their kittypet heritage is rarely if ever mentioned.
 * A Fraction of the Whole is a humorous take on the genre.

Live Action TV

 * Most Long Runner Soap Operas become this eventually.
 * The miniseries Taken.
 * There's an In Universe example from Deep Space Nine: Garak lends Julian a Cardassian epic novel called The Never-Ending Sacrifice, about seven generations of a Cardassian family who all live selfless lives of service to the State. Julian finds it dull as ditchwater, while Garak calls it "the finest Cardassian novel ever written" and the definitive example of the "repetitive epic" genre.
 * In a rather unique twist, the successive series of Black Adder follow (non-consecutive) generations of the Blackadder dynasty.
 * The miniseries Centennial, based on the Michener novel mentioned above.
 * Quantum Leap touches on this with the 3-parter Trilogy, where Sam jumps into a father, then the husband of his daughter, then the lawyer of the daughter focusing on helping her daughter (the granddaughter of his original leapee).
 * In Once Upon a Time Snow White loses her daughter, her husband, and her whole world as the evil queen sends them "someplace horrible," the real world. Emma, Snow White's long-lost daughter, is street smart and resents her biological parents for her abandonment. It takes her own long-lost son Henry to bring her back to the family that she never knew and the idea of the enchanted world they came from.

Theater

 * The family from Rock 'n' Roll by Tom Stoppard aren't immigrants, but it does have the three generations of protagonists with the intermediate one being the odd one out.
 * The Long Christmas Dinner One act, four generations.

Tabletop Games

 * Traveller: Interstellar Wars has a sample campaign called Legacy of War which is like this.

Video Games

 * Age of Empires III campaign mode.
 * Fire Emblem: Genealogy of the Holy War
 * Phantasy Star 3
 * Elemental War of Magic - Start out with a sovereign, end up with an army fielded out of your pants.
 * Romancing Sa ga 2 chronicles a roughly 500-year lineage of emperors. Saga Frontier 2 also lets players follow the multiple generations of the Knights family.
 * Dragon Valor follows one of two paths, depending on whether the first Jerkass protagonist marries the common girl or the princess, and traces his lineage for four generations.
 * Crusader Kings puts you in control of a medieval European dynasty and gives you 400 years to shape them according to your whims.

Western Animation

 * Avatar: The Last Airbender and its Sequel Series The Legend of Korra. Both focus on the latest Reincarnation of a God in Human Form, the Avatar, with flashbacks to events from the lives of prior incarnations. In Airbender Avatar Aang seeks the guidance of Avatars that came before him many times, and eventually encounters descendants of a prior incarnation. The setting of Korra sees a seventy-year Time Skip, wherein many of Airbender's main characters have had Spin Offspring (the most notable being Aang's middle-aged son Tenzin), and have either aged or passed away. Much of The Legend of Korra focuses on the legacy the main characters left after the original series, as well as Korra being guided by Tenzin on her path to becoming the next Avatar.