Good Old Robot

A character has an old robot and deliberately keeps it despite new models being around.

It can be done for practical reasons or just to save money. If it's not, it's always a trait of good characters or, when villains do it, a Pet the Dog kind of trait. This is often An Aesop (and not even a very hidden one) where the old robot will be shown to have a much more developed (and human-like) personality, while the new models will be more able and better looking but unfeeling.

Alternatively, it could be used to establish a character's Perpetual Poverty, alongside their battered spaceship and antique internal-combustion car. After all, whatever the technology level, you can assume a state-of-the-art robotic assistant would be an expensive investment, so an older model might be all their budget allows.

On a more cynical level, this can be down to Special Effects budget concerns. Animating your Robot Buddy takes a lot of effort, but it's worth it to flesh out (pardon the expression) a main character - but why put the same work into background characters when Ridiculously-Human Robots require just a bit of makeup?

Anime and Manga

 * In the Kare Kano play within the manga Steel Snow, the main character keeps 'Antique', an old robot, around because it resembles his first love.
 * This comes up in Ghost in The Shell a few times. The first season of Stand Alone Complex has an episode revolving around an old model of android gynoid which were still popular because they were easy to customise. Another episode has the CEO of a company use what is essentially a box with four legs as his body, as he likes the old-fashioned style.
 * The box isn't actually old-fashioned - the manga explains that it requires extremely sophisticated simulated sensation of body in order to avoid insanity due to sensory deprivation. The man just likes to advertise that he gave up his body to the company, so to speak; they sell organs donated by people who prefer cybernetics, which are cheaper and faster to get than cloned organs.
 * Chobits: Hiroyasu Ueda bought a persocom when he opened his bakery. He fell in love with her, but she then gradually lost her all of her memories. He refused to have her repaired in fear that the persocom would completely lose her memories, much less replacing her.

Comic Books

 * DC Comics' Star Hawkins - Space Detective! His robot secretary, Ilda, is very much an antique model - Star admittedly can't afford better, but he wouldn't get rid of her even if he could. (Except in Twilight [or "Let's make all our goofy sci-fi characters Darker and Edgier"], where he says he'd have junked her if he'd had a chance. But that wasn't the real Star Hawkins.) An even better example is Stella Sterling in Whatever Happened To ... Star Hawkins, who can certainly afford a top-of-the-range robot bodyguard, but prefers Automan, a robot who dates back to the 1960s.

Film

 * Pluto Nash. The titular character's bodyguard robot can't run very fast and his speech is very noticeable Robo Speak. But Pluto keeps him around for sentimental purposes.
 * He's also "incompatible" with Pluto's robot maid.
 * Pluto does get a new one at the end, but only so he can make Bruno his club manager.
 * Bruno also has years of "rill-hopping" experience in him from their smuggling days. Also, compared to the other robots shown, Bruno is a lot smarter.
 * He can also intercept phone calls but can't listen to them himself.
 * In Blade Runner, the character played by William Sanderson has a house full of "misfit toys", so to speak.
 * C-3PO and R2-D2 from Star Wars. Especially C-3PO in the prequels.
 * Other than C-3PO and R2-D2, there are several examples in the Star Wars universe, such as Wee-Gee, the Katarn family droid in Jedi Knight.
 * Taken even further in the Expanded Universe. Luke is at one point given a shiny new R7 astromech to go with a prototype fighter, but soon goes back to his trusty X-Wing and R2-D2.
 * It goes back to the original Star Wars movie (A New Hope). Before the final attack on the Death Star, an X-Wing mechanic notes to Luke that R2-D2 is looking pretty banged up and asks if he wants a new one. Luke declines.
 * The Thrawn Trilogy explains that there are advantages to using old droids that haven't had regular memory wipes, such as the fact that Artoo has worked with Luke's X-Wing computer for so long that they practically have a symbiotic relationship and are much more efficient than the standard. There are also disadvantages - the ship's computer has become so idiosyncratic from this that if another computer needs to scan the ship's data, they need Artoo around to translate.
 * Old Bob in The Black Hole.
 * In I Robot, only the newer models of robot begin attacking humans. The older models actually fight against the new models briefly due to their un-updated programming.
 * This was the plot of Cherry 2000; the male protagonist accidentally breaks his Robot Girl, and her model's out of production. Instead of getting a new model, he hires an Action Girl to take him to the abandoned factory in the post-apocalyptic wasteland, so he can find another Cherry-model to install the backup memory chip into.
 * In Real Steel, Atom is a previous generation sparring robot that was stored whole and functional (but uncleaned) in a parts depot. He has different strengths and weaknesses from current top of the line arena fighters, which allows him to survive when facing them.
 * Some of his strengths have nothing to do with being outdated. Since he was built as a sparring bot, not a fighter, his body is specifically made to be highly resistant to damage. On the other hand, his physical strength is very low for a robot (also intentional). Basically, he can take a punch but not give one.

Literature

 * Isaac Asimov likes this trope.
 * From Foundation: R. Daneel Olviaw, even before
 * In "The Bicentennial Man", Andrew (later known as Andrew Martin) is owned by the Martin family. Most other robots are leased and recycled after a number of years. After Andrew's "individuality" annoys the CEO of U.S. Robotics, the company buys back all old robots (the Martins refuse to sell) and destroys them. The company even later begins to reduce the intelligence of the robots, with all higher functions being done by central computers in communication with the robots. Sort of like PCs today, where you can buy netbooks and/or browser OS.
 * In short story Light Verse, a wealthy socialite and artist refuses to fix her old robot butler, finding his eccentricities charming,.
 * Bollux in the Star Wars ''Han Solo Adventures" trilogy by Brian Daley.
 * Bollux is actually a slight subversion, as his only real use is as a mobile hiding place for a highly-advanced hacking/data droid, a Trojan Horse if you will.
 * In Star Wars: The Old Republic: Fatal Alliance, the pirate Jet Nebula has a trusty old droid named Clunker with a broken vocoder. The only way he communicates is via an old military code, consisting of hand signals. Jet prefers it that way and thinks Clunker intentionally broke his vocoder (something about "if you didn't reply to an order, then there's no proof you heard it").

Live-Action TV

 * The last part of the Red Dwarf episode The Last Day centres on this.
 * In Power Rangers SPD, the robot dog RIC (Robotic Interactive Canine.) Run down and broken, with replacement parts long out of production, he was given to making any sound but dog sounds, and annoyed the Rangers until he jumped into Mecha Mooks' fire to save Syd. Though she had been first in line to just recycle him before, now Syd couldn't bear to, and got the tech-savvy Bridge and Boom to work on him. The result is a Do-Anything Robot that even turns into a "K9 Cannon" for a Finishing Move... though a lot of fans preferred RIC the way he'd been before!
 * An episode of The Twilight Zone featured a down-on-his-luck boxer in an age when all boxing was done by prizefighting robots. His old Mark 3 boxer-bot was no match for the new Mark 7s that littered the profession, but darn it, the Mark 3 was his robot.
 * This episode was based on a short story by Richard Matheson. The story was later loosely adapted into a film called Real Steel.

Video Games

 * Anachronox. PAL-18 was originally built as a toy (the series is considered valuable collector's items) but is custom-equipped with hacker software and functional weapons. And Mystech capability. And self-awareness. And the personality of a bratty eight-year old. All in all making him far more useful than anything manufactured recently.
 * While it isn't touched on much in the games, the Mega Man series can be seen as an example. In the Classic and X series the heroes have to defeat newer and newer models of robots, knowing that they themselves stay the same.
 * The story of the X series partly revolves around the fact that the only reason X and Zero can save the world is because they are old robots: Reploids are created with a newer manufacturing process (and lack their Restraining Bolts) that make them easier to succumb to The Virus and do evil.
 * Joey in Beneath a Steel Sky. Even though he's built from scrap parts found in garbage dumps in the Australian wasteland where Roberts' tribe lives, he manages to interact with, even outsmart, more modern robots/programs. Also, his circuit board seems to be compatible with most robots they encounter.

Western Animation

 * Helper from The Venture Brothers is certainly of the money-saving variety. Dr Venture prefers to repair or reuse his father's old tech than invent his own.
 * Still not the straightest example though, since Helper seems to be the only robot in that universe.
 * More or less the premise of The Brave Little Toaster. More or less.
 * Happens on an episode of The Jetsons, when Rosie is apparently outclassed by a later model of robot, and runs away when she sees a salesman giving them the hard sell.
 * Carl from Meet the Robinsons is the lowest tech thing the family has, apparently built when Lewis was just a kid. His son inherits it.
 * The show Cubix Robots for Everyone. The main robot, Cubix, was a pile of junk that the main human started tinkering with.
 * Bender of Futurama is obsolete as of the debut of Robot 1-X in "Obsoletely Fabulous." The episode went through a complicated process of getting Bender and the older robots to accept the 1-X, and then the 1-X inexplicably disappeared and hasn't been seen since.
 * 1-X reappears in the movies, but considering it got sliced in half, it seems unlikely that it'll appear in the new season.
 * It has reappeared in the new season... in Robot Heaven.
 * Dr. Wakemn of My Life As a Teenage Robot keeps XJs 1-8 around for no other reason than apparent sentimental value.