In Magic: The Gathering, the ability changeling gives a creature all creature types. This includes Ninja, Pirate, Zombie, and unfortunately just Construct.
The World Of Synnibarr is built around this concept, featuring ninjas, Golden Tiger Mages, gods as player characters, and Giant Mutant Fire Clams. And grizzly bears that shoot lasers from their eyes. And a god of rock 'n' roll.
Rifts runs neck and neck with Synnibar for weirdness/awesomeness. It gives us techno-wizards on flying surfboards shooting railguns, vampire-hunter cowboys herding dinosaurs, extraterrestrial bikers, genetically engineered humanoid dogs, Alien Cyborg Samurai, Crystal Dragons, Undead Super Soldiers, Psychic Horses, and a power struggle with the Four Horsemen of the Apocalypse on one side, and King Arthur and his knights in power armour backed up by dragons, demigods and an amnesiac Egyptian goddess on the other side. Oh, and humpback whales who can learn fly-fishing.
Torg is a crossover game where Action Adventure Tropes are real and cyberpunks fight minions of the Cyberpope and their plant-zombie minions with the help of pistol-wielding mystery detectives and heroic knights.
Exalted In the beginning the Sun the Moon and the stars got tired of there Eldritch Abomination bosses so they sent Gilgamesh, Enkidu, The Doctor and, the entire cast from avatar the last airbender(as well as the cast of legend of Korra). After killing some of them and becoming ghosts, the rest were horribly mutilated and imprisoned in Azathoth. Now it is Fire-breathing cyborg dinosaur precursors with super science vs Communist ninja robots with lightsabers from outer space! It's a game where Cuchulain is riding around in a Gundam to fight Vincent Valentine, who has been enslaved by Emperor Palpatine, while John Talbain and an army of Celts is going to war with the Roman Legions, who are led by the cast of Ranma 1/2. And the spawn of Queen Mab and the Joker want to make the world into a toxic rainbow slush. Meanwhile, Nyarlotep gives Peter Parker some of his and others superpowers so the can breakout of Azathoth. If it's cool, then it's supposed to be ganked and put into the game! In other words, Best. RPG. Ever. There's a martial art for sadomasochist lesbian stripper ninjas.
Dreadnoughts (essentially, Mecha piloted by practically undead super-soldiers) come dangerously close to being actual zombie robots, as well as the aforementioned Necrons.
Necrons could be considered the very page title. The zombie robot part has been explained, wraiths are quite similar to ninjas in their stealth and material phasing abilities, and Necrons often partake in pirate raids.
The Blood Angels now have Librarian Dreadnoughts, giving them a Zombie Humongous Mecha Cyborg Wizard. That can fly.
At least one of the unofficial harlequin lists had Harlequin Wraithlords which indeed was a 12 foot tall psychedelic Space Elf Ninja Clown Zombie Robot. Depending on fluff it could be a pirate.
Speaking of the Eldar, here is a fitting description of their heavy infantry, the Striking Scorpion Aspect Warriors: power-armored chainsword weilding gunfaced jungle ninjas. Their squad sergeant can fight with an insect-style armor-piercing pincer incorporating a shuriken-firing SMG, to boot.
What about the Exodites? Amish dinosaur-riding cowboy Wood Elves IN SPACE.
And various methods when you just have to absolutely, positively, kill every single motherfucker on a planet.
Warhammer has a rather awesome example of this trope in Luther Harkon (a Vampire) and his Zombie Pirates of the Vampire Coast. His crew roster includes Vampire Pirates (himself, possibly others), Zombie Pirates, Zombie Ogre Pirates, and Zombified Sea Monsters. Oh, and the zombies still use blackpowder pistols, muskets, swivel guns, cannons, and Queen Bess, a former Hellhammer Cannon.
Long Drong, an eyepatched, parroted, dwarf pirate.
While not a part of 'canon' Dungeons & Dragons, the variety of races, templates, and character classes available can result in ridiculous combinations, like a Fiendish Dragonkin Vampiric Samurai Half-Orc Fighter/Wizard/Monk/Shadowdancer. Or a sandwich. Or a chicken slaad sand witch. This is frequently the work of a Munchkin, however it's often ostensibly done for "role playing" purposes. There's even a "type pyramid" listed in one book that ranks just how hard it is to use this trope on various monster categories.
The ultimate example of this trope came from a specific thread on the Dungeons & Dragons character optimization boards. The end result was A Zombie Ninja Pirate Jedi with a Demonic Cyborg Midget Monkey Schoolgirl sidekick and a small crew of Mutant Zombie Sea Bass, riding in a Transforming Robot Dinosaur, armed with Lightsabers and Eye Lasers. Sadly, the design was considered too dangerous to ever create as it could easily destroy the world.
The latest edition offers as one of the playable races the Warforged, which are essentially magical robots. Then, they had an expansion where you can play a deceased-but-reanimated version of any playable race, like an intelligent zombie (at at higher levels can become a ghost too). So you can now play an actual Zombie Robot Ghost!
Actually using a Warforged ninja as the base creature and class, then gaining the zombie template(which can be applied to any corporeal creature) from any creature whose create spawn ability turns you into a zombie, the Emancipated Spawn prestige class(to regain your ninja abilities) and finally the Dread Pirate prestige class can turn you into a genuine Ninja Pirate Robot Zombie.
Teenagers from Outer Space, an 80s game based on Anime, pits the characters in an alternate Earth where high schools are overrun with aliens - every kind you can imagine - and teenage humans head to the mall to buy dangerous weaponry in order to wage wars with their classmates. The only rules, besides the bare game mechanics, are the ones that the GM chooses to impose, so it wouldn't be uncommon to see a telepathic raygun-wielding teddybear driving a flying saucer down Main Street while listening to the Pretty Things.
In the early days, they published a few modules featuring Sam Haight, a ghoul/werewolf/mage whom, Game Masters were told, the player characters were not allowed to kill. After a while even his creators got tired of him, killed him off, and then casually mentioned that his soul had been forged into an ashtray in the underworld.
The toy line/tabletop game XEVOZ featured a figure called Skull Jack that was a Skeleton-Pirate-Samurai with laser vision.
Characters in Maid RPG can easily end up as this, depending on what you roll and how many special qualities you use. If you're willing to try for it, it's perfectly possible to have, for instance, a Zombie Catgirl Spider Demon.
This is in large part the appeal of the Legend System, which features a Ninja Pirate Zombie Kamen Rider as one of the saner possible character builds.
If you're willing to be a ghoul or skeleton instead of an actual zombie, you can have a LITERAL Ninja Pirate Zombie Robot with I Am Ten Ninjas/Swashbuckler/Undead/Sentient Construct. Better yet, this is a completely legal build for a character to take.
The card game Smash-Up is built around this. Each player gets two mini-decks, each based on a theme (ninjas, pirates, zombies, robots, etc) and shuffles them together to create his play deck.