The name "HiME" in Mai-HiME means "Highly Advanced Materializing Equipment", as explained in the opening sequence; this is a play on the Japanese honorific "hime", used to address someone as "princess", and refers to the titular HiMEs' ability to materialize objects out of hammerspace (or, as Techno Babble holds it, out of photons). While the acronym may seem forced, being part of a much more convoluted, five-part bilingual pun certainly redeems it.
Fun with Acronyms is even more evident in the Mai-HiME manga, which introduces two additional types of HiMEs: Perfect Realization of Independent Access (PRINCESS) and Quaint Elemental Enchantress (QUEEN).
Let us not forget Miyu Greer: Multiple, or Merciful for her Mai-Otome counterpart, Intelligencial YggdrasilUnit.
And while on the subject of robots, how about the Boomers from Bubblegum Crisis? Originally this wasn't an acronym, but the term VOOMER (which is pronounced the same in Japanese) was an acronym in Bubblegum Crisis 2040.
The organisations SEELE, GEHIRN, and NERV in Neon Genesis Evangelion (which are German for soul, brain, and nerve respectively), though always written with capital letters, apparently do not stand for anything, but as this trope works in both senses this would be more like a subversion.
RahXephon gave us Tereno Empireo Rapidmova Reakcii Armeo. It appears to be Esperanto for "Earth Federation Rapid Reaction Force", judging from the contextnote it's actually mostly Foreign Sounding Gibberish.
Mobile Suit Gundam start with only AMBAC (Active Mass Balance Auto Control), but Retcon add Mobile SUIT (Mobile Space Utility Instrument Tatical) and Mobile ARMOUR (Mobile All Range Maneuverability Offence Utility Reinforcement).
From Mobile Suit Gundam Wing, we have GUNDAM (GUNDAnium Mobile suit), MOBILE Suit (Manipulative Order Build and Industrial Labors Extended Suit), Mobile DOLL (Mobile Direct Opertional Leaded Labor) and ZERO system (Zoning and Emotional Range Omited system).
∀ Gundam has mobile suit call SUMO (Strike Unit for Maneuver Operation) and FLAT (Flexible Ladder Actuator Technology).
Not to be outdone, ZAFT (Zodiac Alliance of Freeedom Treaty), the military arm of PLANT (People Liberation Acting Nation of Technology, formerly Productive Location Ally on Nexus Technology), seems to name almost all of their high end mobile suits as acronyms, featuring the ZAKU (ZAFT Armored Keeper of Unity), the GOUF (Guardian Of Unity Forerunner) Ignited, and the DOM (Defensive Obliterator Magnificent) — note that all of these are acronym-ized versions of the Zeon suits from Mobile Suit Gundam. Even more confusingly, almost all their other mobile suits (GINN, BuCUE, LaGOWE, BABI, DINN, GOOhN, ZnO, CGUE, GuAIZ, etc.) seem to be acronyms that have no actual meaning. One of aforemention variant of CGUE is call DEEP Arms ( Directional Energy Emission exPerimental Arms). Their special forces group is also known as FAITH (Fast Acting Integrated Tactical Headquarters).
In a possible subversion, the military forces of Earth are officially known as Oppose Militancy & Neutralize Invasion (OMNI) Enforcer, but no one ever refers to them as such, usually settling for Earth Alliance Forces or simply Earth Forces. Similarly, the Earth Alliance's shadowy secret controlling organization LOGOS is always capitalized, but apparently stands for nothing (like Evangelion, it's actually a reference to a theological concept). However, their main headquarters of JOSH-A (JOint Supreme Headquarters Alaska) is potentially an extreme case of this trope, as, despite its spelling, everyone pronounces it as "Joshua".
Weapons systems acronyms in the series include the DRAGOON (Disconnected Rapid Armament Group Overlook Operation Network) system, the METEOR (Mobile-suit Enabled Tactical EnfORcer) support system, and the GENESIS (Gamma Emission by Nuclear Explosion Stimulate Inducing System) superlaser.
Finally, the title itself refers to Superior Evolutionary Element Destined-factor (SEED factor), which apparently gives a person the abilities needed to advance the evolution of mankind.
Gundam 00V has GRM (Generation of Reborns Mobile suit - pronoun as "Garm") Gundam and Cherudim Gundam SAGA (Special Assault Gundam Arms)
The original Japanese version of Yu-Gi-Oh! GX has SAL (Super Animal Le(a)rning), a monkey that was being trained to duel using technology. It should be noted that it is pronounced "saru", which is Japanese for "monkey".
General Axis Motorized Battle Exoskeleton Equipment. The weaker mecha of the grunt soldiers that Sara must join for a few episodes.
Ministerial Instrument of Mercurion Interface Core, the plot's Human Resources and the device that allows Strains to operate.
GaoGaiGar's GGG(organization defending humanity from Zonders) stood for Gutsy Geoid Guard. In season 2, it received a new name(as well as an orbital base): Gutsy Galaxy Guard.
Though it was almost certainly unintentional, Ghost in the Shell has the rather unfortunate acronym "GITS"; by way of explanation, git is a coarse British insult. The fact that [Stand Alone Complex changes this acronym to GITS SAC does not help matters...
Let's not forget "P.A.N.D.R.A." and whatever it stood for again. Note that when the Japanese pronounce it they normally insert an (unstressed) "o" between "d" and "r", thus "pandora".
Digimon has DORUmon which stands for Digital ORUnknown monster
Code Geass gives us the rather unintuitive acronym, "F.L.E.I.J.A", which stands for Field Limitary Effective Implosion Armament. The "J" doesn't stand for anything; it is only there to facilitate the word's pronunciation as "Freya". If the reference to the Norse goddess was intentional, one wonders why they didn't just call it the Fission Reaction-Enhanced Yield Armament.
There's also the Superlative Extruder Interlocked Technology Exclusive Nexus, which is the Guren SEITEN. Of course, SEITEN isn't a word in English, but in Japanese, it means Eight Elements... which is what the start-up screen calls it. In English. That's a surprisingly high-level of knowledge of Japanese language from a Britannian engineer.
Not to mention the fact that the SDF-1 Macross itself was formerly known as Alien Space Ship One.
The novels of the dub, Robotech, give a backronym for Veritech: Variable Engineering and Robotic Integration Technology.
The FAST Pack, while never mentioned anywhere, is actually a real-life acronym for aerodynamic external fuel tanks used by the F-15C (an F-15 variant that came out around the same time the first Macross series was made): Fuel And Sensor Tactical Pack.
Macross Zero gives us AFOS, which, presumably, stands for Artifact From Outer Space
In the Macross universe, the United Nations Space Navy is abbreviated as UN "Spacy." By the time of Macross Frontier, a "New" has been appended to it. Therefore, people make a habit of calling it NUNS.
Darker Than Black has PANDORA, the Physicalquantity Alternation Natural Deconstruction Organized Research Agency.
The mecha from Sora Wo Kakeru Shoujo are called QT Arms (which is a cheesy enough name in itself); the name is also an acronym for Quantum Technology Advanced Reinforced Maneuvering Shroud.
The same series' Latex Space Suits are called Q-Tectors; their acronym being Quantum Transducing Environment Crosslink Terrain Operational Reinforcer.
Chirality has main character Carol, whose name stands for Chirality Artificial Recombine of Life.
Armored Trooper VOTOMS, the armored trooper is result from project call Vertical One-man Tank for Offense & ManeuverS.
In Full Metal Panic!! Tuatha Dé Danann has system call TAROS for Transfer And Response Omni-Sphere.
In Funimation's Gag Dub of Keroro Gunsou, Keroro is leader of "the Advanced Recon Mission Prepatory Invasion Terror Platoon", whose acronym is unfortunate, but is nonetheless intentional on Funimation's partnote In the Japanese version, they are simply called the "Keroro Shoutai", or "Keroro Platoon"..
In Naruto the ANBU, or Ansatsu Senjutsu Tokushu Butai (Special Assasination and Tactics Squad)are elite "black-ops" ninja in porcelain masks. ANBU is also Japanese for Dark Side, which makes sense given the fact that they carry out the missions for which Konoha will accept no official responsibility.
In Ultimate Girls, the source of the girl's energy is 'Maiden, Oh don't look at me please, Energy' or M.O.E. It is also produced by Masters Of Entertainment.
The Guest Star Party Member of the fourth and fifth seasons of Slayers is a young prince named Pokota, which is actually an acronym of his real name, Posel Korba Taforashia.
Haruhi Suzumiya: And how could we possibly forget the "Sekai wo Ooi ni Moriageru tame no Suzumiya Haruhi no Dan"?
There are two English translations: "Spreading Excitement All Over the World with Haruhi Suzumiya Brigade", used by the anime, or the Ascended Fansub "Save the World by Overloading it with Fun: Haruhi Suzumiya Brigade", used by the manga and light novels.
Meanwhile, fans have decided to backronym it into "Slaves Of Suzumiya Brigade".
Yaoi stands for "yama nashi, ochi nashi, imi nashi" (no highs, no lows, no point), but among fans, there's a joke that it stands for "Yamete! Oshiri ga itai!" (Stop! My ass hurts!)
Only in the so-called "dub". In the original Japanese, the company is called "Holy Nightmare".
The GA in GA Geijutsuka Art Design Class stands for "Geijutsuka (Art Department) Class A", though Tomokane's guess, "Graphic Arts Design Class is pretty reasonable. Kisaragi's (albeit that was Tomokane messing with her) "Go for it, Artists!", not so much.
Episode 9A of Sakura Trick is titled The SBJK of New Year Debuts. So what is SBJK? "Shitto Bukai Joshi Kousei", or "Deeply Jealous High School Girl. Some fansubbing groups translated to "Super Berserk Jealous Kid" or "Super-Begrudging Juvenile Kitten" to keep the acronym.