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."
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."
Smash Up has a minion called "King Rex." It's a Tyrannosaurus Rex.
The producers of simsense recordings in the world of Shadowrun sometimes have to whip up portions of those recordings from scratch rather than live-record it, usually because sensations associated with spellcasting or astral phenomena can't be captured by sim-tech. Industry jargon refers to such computer-generated patches of experience as pseudosim.
In Delta Green, one antagonistic group are Americans Against Covert Enemies, basically a racist hate group that's secretly backed by a ruthless and very well-connected Mythos cult. The sourcebook they're covered in contains a list of their preferred targets, which mentions Islam five times even before discussing their direction after the September 11 terror attacks.
The D&D supplement Complete Psionics has the Deja Vu power (which causes the target to repeat their previous action) listed twice. Since the second entry shows up several pages later, with no indication of being a repeat (other than being out of alphabetic order), it's entirely possible to read it and go, "Hey, didn't I read this before?"
From Yu-Gi-Oh! the card Red-Eyes Fusion, which special summons a monster and lists that it can only be used once per turn; despite the fact the card itself prevents any further special summons that turn hence making the limitation redundant.
Also, the card Harpie Lady Phoenix Formation will inflict damage among the highest attack of your opponent's destroyed monsters, with the addition of "Your choice if tied". Since if the attack is tied it will do the same thing no matter what, it's a completely redundant choice.
Prior to the addition of problem-solving text, many cards were an example of this, especially the earliest cards. Probably the most extreme example was declaring "Regardless of position" for monster destruction effects.