Legacy of Service

Blackadder: You're fired.
Baldrick: But my lord, I've been in your family since 1532!
Blackadder: So has syphilis, now get out.

—Blackadder

Sometimes, there are servants who do get very attached to the master family. So much that their children follow in their footsteps and continue serving the family's descendants. Hence the reason why there are servants who come from a very long line of faithfully serving their masters.

Common in anime and manga, since 'servant families' were common in Feudal Japan - some of those relationships remain today, if only symbolically, and often pop up to be played for drama, action or romance. Their masters might also have some sort of particular affection for their servants (which the servants can return), leading to relationships such as Heterosexual Life Partners (or, less common, Platonic Life Partners or Like Brother and Sister).

Such servants are very likely to stick with the master should they ever become an Impoverished Patrician, like the Old Retainer. The servants can take any form, be it a Maid, a But ler, The Igor, the Girl Friday, or the Kindly Housekeeper. Can lead to Bodyguard Crush. Keep in mind, of course, that the trope need not extend merely to servants, and that anything from lawyers or flower girls can be subject to this, too.

Examples of Legacy of Service include:

Anime and Manga

Kaze no Stigma, where the first Arc is powered by the rebellion of a family of wind-ninjas who have been serving the Kannagi Clan for centuries, and have finally gotten tired of it.
Ouran High School Host Club: Mori is the son of a family that has served Honey-chan's family since the Warring States Era, and despite the relationship being officially dissolved, he continues to serve and protect Honey-chan with supreme loyalty.
Yu-Gi-Oh: The Ishtar family has been serving the Pharaoh for thousands of years, most of that living in an underground labyrinth protecting his tomb. Resentment over this is a huge part of what fuels Marik's Start Of Darkness.
In Fullmetal Alchemist, Ling's bodyguards Lan Fan and Fu come from a family that has served the Royal Family for a long time.
- There is also the flower lady who passes on Olivia's message to Mustang, who's family has SERVED THE ARMSTRONG LINE FOR GENERATIONS!
The Bakers have served the Burtons for centuries in Madlax.
In Mouse, Mei Momozono came from the family that served Sorata Muon's family (Mouse House) for generations. For her it was more fun, though.
The Battle Butler Sayoko Shinozaki from Code Geass, she is the 37th sucessor of the Shinozaki school.
Negima Neo turned this into (one of) Setsuna's motivations for protecting Konoka.
Subaru Konoe from Mayo Chiki comes from such a line of butlers. The position is traditionally reserved for males, but Subaru has no brothers, and so Subaru has to jump through numerous hoops (most notably posing as a boy in public) to prove herself worthy.

Comics

The original story for Bruce Wayne's butler, Alfred Pennyworth, whose father, Jarvis, had been Thomas Wayne's butler. This particular version of Alfred was canon until Frank Miller's Batman: Year One, which established that Alfred had himself been Thomas Wayne's butler/valet, and had worked for the Wayne family since before Thomas and Martha Wayne were killed.
Doctor Strange's manservant Wong is from a family whose ancestor, Kan, pledged that the firstborn males of his family would be dedicated to the service of the Sorcerer Supreme.

Fan Works

The author of Top Dog creates one between the Hyuugas and the family of the Fourth Hokage in the Naruto branch; this immediately colors Hiashi Hyuuga's reaction to Naruto once he finds out his parentage.
In Progress, Princess Luna's maid Sundance is apparently descended from one of these. According to the side-story "Celestia vs. Time", Sundance's great-grandmother was a servant at the palace as well.
In Undocumented Features, the Dragonaars have been this for the royal family of Gamilon, the Desslers, for centuries.

"For every Dessler, a Dragonaar."

Film

Young Frankenstein: "My grandfather worked for your grandfather."—Igor
In Forrest Gump, Bubba's family has apparently been in service for at least a century. The montage which shows different generations serving seems to imply that they are serving different generations of the same family. In this case, it's treated as a bad thing, since their service originated during the time of slavery.

Literature

The Butler family in Artemis Fowl has been serving the Fowl family for a long time (the earliest recorded relationship between the two families dates back to the Third Crusade).
Afanasiy Zyukin from The Coronation is a butler in the third (I think) generation.
Thomas' family in The Infernal Devices is a long line of people with a touch of the Sight, which enables them to serve the Nephilim.
Kitty Goes to Washington features a family that has served a female vampire for centuries. It turns out they are all descended from the two children she had before she became a vampire.
From The Hound of the Baskervilles, John Barrymore, whose family has served the Baskervilles for generations.
In the Liaden Universe, the family firm of dea'Gauss have served as attorneys to Clan Korval through many generations. One of the prequels reveals that it was a dea'Gauss who did the paperwork for the founding of the Clan, centuries ago, and Korval has had them on retainer ever since.
The Stewards of Gondor, sort of. Being a family tasked over to watch over the throne in absence of a king, they had been waiting for when the Rightful King Returns and should have recognized Aragorn as the rightful King of Men, but Denethor has other ideas.
The Brands of David Eddings' Belgariad are hereditary servants to the Kings of Riva, serving as a sort of chancellor - handling the day-to-day drudge while the king makes the big decisions. So dedicated are they to their duty that upon assumign office, they abandon whatever name they had before, becoming known simply as 'Brand' (which was the name of the first one to hold the office). Similar to the The Lord of the Rings example, they've spend a long time taking care of Riva and its throne while waiting for the return of the true king, but once he DOES show up, they never falter, and continue to serve faithfully. (With one notable, but quickly-corrected exception.)
- The prequels mention Polgara's servants while she was Duchess of Erat (she technically still is, but in practice Erat is no longer a duchy and the house has been deserted).
Subverted in the Sharon Shinn short story "Bargain with the Wind" by way of another trope: My Grandson, Myself. Nettie the Old Retainer housekeeper is actually an earth spirit who watches over the family. At the end of the story she recommends her "niece", Norah, as a replacement housekeeper, and then changes her form from an old woman into a young girl.
Although it's only in the first/second generation it seems likely that the Clinkscales and La Follet's will become this for the Harrington clan. In the case of the Clinkscales two generations have served her as Regent and Honor has actually formally adopted the clan as an extended part of the Harrington clan. In the case of the La Follets at least four members of the clan have served her in various positions (two male members as bodyguards and two female members as maids/advisors).

Live Action TV

A Blackadder always seems to end up with a Baldrick as a servant or something or other regardless of his status. What's interesting about this is that we actually see the bond being formed in the first episode, something we don't usually see in other examples of this trope.
On The Nanny, Niles' father was the butler for Maxwell Sheffield's family before Niles himself became Maxwell's butler.
Hudson, Rose and Mrs Bridges from Upstairs, Downstairs all came from the Southwold Estate and serve the Bellamy family for more than thirty years without appearing to age at all. Other servants come and go - Ruby and Edward being pretty long-standing - but these three are rather immortal and look like they will outlive even Sir Richard...
In Samurai Sentai Shinkenger, four of the Rangers come from families that serve the clan of the fifth, Shinkenred.

Tabletop Games

Forgotten Realms has some long-runnners. Cormyrean court mages were direct descendants of the elven magess Alea Dahast and Baerauble Etharr, the first High Wizard of Cormyr from 26 DR, until Vangerdahast Aeiulvana retired in 1372 DR, followed by Caladnei—the first chief War Wizard supposedly not of this bloodline.

Video Games

The Shiekah of The Legend of Zelda: Ocarina of Time has ever been faithful to the Royal Family of Hyrule, and has served them for generations as retainers, with Impa being the latest in a long line.

Webcomics

Girl Genius has two such families named so far:
- Violetta is a member of a family of Smoke Knights who have served Tarvek Sturmvoraus's family for generations (her family being a somewhat lower-ranking branch of his).
- The Von Mekkhan family has been serving the Heterodynes for generations as their Senechals, essentially family retainers who help maintain the Castle.
- Also, Played for Laughs with the kid from a family of hereditary grave robbers.