GURPS Illuminati University actually has several Department of Redundancy Departments.
Naturally, Alpha Complex in Paranoia actually has a Department of Redundancy Department.
And many other variations on the theme. "Oh, this is the Complex Supply Bureau. You want the Bureau of Complex Supply."
An actual RPG session incident, when the GM wanted to make a particular detail very clear to the player: A female soldier with a rifle, pointed at you. She's wearing a green-camo uniform, complete with a rifle, which is pointed at you. The rifle appears to be a high-caliber automatic, and is pointed at you. The soldier is guarding this position, and is pointing her rifle at you. From a cursory study, she appears to be hostile — evidenced by the fact that she has a rifle pointed at you. She commands, in an aggressive tone, "Put your hands up! I have a rifle pointed at you!" Also, she has a rifle pointed at you.
It doesn't always work though. In one recorded instance, a Shadowrun party crawling through an oil pipeline was subtly warned four times about all the oil in the oil pipeline, but that didn't stop them from lighting their blowtorch. (One character survived the explosion but was knocked out and drowned in the harbor outside.)
The ever-troperiffic Warhammer 40,000 brings us Ferrus Manus—whose name means "Iron Hands"—Primarch of the Space Marine chapter the Iron Hands, who actually has iron hands.
The chant of the chaos marines "Blood for the Blood God" and "Skulls for the Skull throne".
Special character Canis Wolfborn is a Space Wolf, a Wolf Guard in Harald Deathwolf's Great Company, Lord of the Wolfkin, was literally Raised by Wolves, wears a wolf tail amulet and a wolftooth pendant, and rides a Fenrisian Thunderwolf into battle. This and similar examples led to a minor meme where random nouns and names are replaced with WOLF WOLF WOLF.
The Chapter-creation rules in Deathwatch allows for the name-generation table to spew out some pretty tautological Chapter names, like the Guardian Guard, War Warriors, Bloody Blood, and... Death Death.
In the fantasy world Glorantha (featured in, among other things, the RPG RuneQuest) the local equivalent of China is bordered by the Shan Shan Mountains. In one Chinese language - I have forgotten which - "shan" means mountain. So they are the Mountain-Mountain Mountains. Did we mention that they are really high and impassable?
Due to some confusion when he first introduced himself, Ravenloft's most infamous lich is referred to as "Azalin Rex" in official court documents of his domain of Darkon. Invokes this trope, as "Azalin" is actually a mangling of his old Oerth title of "Wizard-King", thus making him Darkon's "Wizard-King King".
In the RPG Orbital, one space ship has "two emergency low berths for emergency use", and in outposts, "Individuals or teams will be regularly rotated back to the main installation on a regular basis".
The Low Life card game Dementalism is described on the back of the box as, "An ingenious game of ingenious ingeniousness."