Magitek is a setting aesthetic based on the idea of melding magic and technology together in some fashion. If this sounds rather vague, that's because there's at least four different ways of doing this that commonly appear, but all share this basic aesthetic.
Method one is where you start with an existing technological device and then either add magic to it or use it to interact with magic in some way. For example, a PDA or computer hard drive that doubles as a magical grimoire, a gun enchanted to produce an endless array of bullets, or a car that can fly. This is particularly common in "urban fantasy" settings, since they tend to have magic existing alongside but hidden from "the real world". It's also a common feature in more "kludge-up" settings since, again, you have magic and technology existing side by side, so somebody's going to see if they can be brought together.
Method two is where you have something that looks scientific, but really runs off of magic. This is more common in "lower-tech aesthetic" settings like Clockpunk, Steampunk, and Dieselpunk, as it allows the technology to equal or exceed the capabilities of real-world tech despite using a much more primitive set of base technology. This is perhaps the rarest form of magitek, as most such settings don't really want to admit that their "technology" is really Magic-Powered Pseudo-Science.
Method three is where you meld magical and technological components together to achieve a greater whole - this is perhaps the most iconic form of magitek, as it clearly respects both halves of their "make-up". Neither aspect functions alone, but only together do they shine.
Method four is where you have magic being industrialized; it's so common and ubiquitous that it has developed to take the place of technology entirely, even if the viewers can still see the roles; crystal ball networks replacing telephones/videophones/radio/the internet, enchanted carriages replacing real-life vehicles, enchanted bows or blaster-wands replacing guns, and so forth.
Common long-running plot hooks for such settings involve mana or some other vital magical resource running out, or otherwise being fought over, and common magical devices turning against their users (especially if bound demons are involved).
This is actually a fairly popular aesthetic for fantasy settings, and so there's quite a few examples out there, both directly /tg/ related and otherwise.
- Dungeons & Dragons in general has built up a huge list of "industrialized magic" examples across the many settings and over the years. However, due to Medieval Stasis, either the setting totally runs with it (Spelljammer, Eberron), or else it tends to be restricted to lost civilizations or out-of-the-way places (Forgotten Realms, Mystara).
- The Half-Golem is a template-race from Dungeons & Dragons 3rd edition that is essentially a magitek cyborg.
- The Warforged is a sapient golem, making it essentially a fantasy robot race, which has led to a stigma that they cannot shake off.
- In the Hollow World subsetting of Mystara, the various technological items are actually running off of divinely granted magic, making them little more than enchanted items with funny appearances. This is intended to enforce the Medieval Stasis of the setting, as each "advanced" culture in the Hollow World is the last remaining preserve of a civilization that wiped itself out earlier.
- The Deadlands setting makes use of types one through three. The various Steampunk technology draws its power from burning Ghost Rock, which is literally the spirits of the damned compressed into magical coal. This also allows it to warp reality to allow things like clockwork-based cybernetic implants to function. The Mad Scientist class thinks it's doing science, when in reality their inventions are powered/given to them by demons whispering schematics and arcane secrets into their brains whilst they sleep. The Metal Mage archetype is a case of Deadlands multiclassing where you combine a Mad Scientist with a Huckster, and which invented a lot of spells specifically relating to technology (from being able to conjure simple gadgets to more rapidly build gadgets to dismantling gadgets in the field).
- RIFTS has the Techno-Mage class, which is an engineer-wizard who specializes in enchanting existing technology and building technological items that run off of/incorporate magic.
- Iron Kingdoms distinguishes itself by the fact all of the super-tech it uses is shamelessly powered by/based on magic.
- Exalted has a lot of examples of the "science and sorcery combined" style, reaching its peak in 2nd edition (magic-powered power armour and fighter jets, artificial limbs, and clockwork-based golem-androids) before it was dialed down in 3rd edition.
- D20 Modern quite obviously uses the "enchanting existing tech" approach, given it's the epitome of urban fantasy gaming with a D&D origin.
- There's too many examples of the "enchant existing tech" approach in the World of Darkness to count, but Mage: The Ascension stands out for using the "magic powered pseudo-science" approach, having the world-lore that technology is just another style of magic which came to dominate the "reality paradigm".
- CthulhuTech blends science and sorcery together so hard that it's impossible to tell where the difference actually lies. Fitting, given that H.P. Lovecraft basically stated that "magic" in his stories was merely a hyper-dimensional science that humanity doesn't understand.
- Warhammer Fantasy has two factions that both use the "meld magic and tech" style together; the Skaven have elaborate electrical engines fueled by warpstone, which is essentially daemon-possessed plutonium, whilst the Chaos Dwarves build elaborate machines that only work due to being possessed by daemons. Of the two, it's hard to tell whose tech has more inherent issues. Chaos Dwarf tech demands blood sacrifice to run and wants to kill its operatives even when fed, Skaven tech just has a tendency to explode.
- Magitek is rather prevalent throughout the Warhammer 40000 universe, as many of the most advanced technology draws upon the Warp in some form or another. Of course, this is a grimdark universe and Warp energy corrupts the fuck out of everything, so great pains must be taken to use said technology with due precautions/as little as possible. Or alternatively embrace the corruption and become a slave to darkness, but that's another bag of dicks.
- Shadowrun is what happens when you add type 1 magitek to a cyberpunk world.
- Magitek gets its name from Final Fantasy 6. Magitek is used in two ways. The first is Magitek armor. For the player it allows them to select three elemental attacks and a one person healing ability. While a half-esper gets a bio-blast, the ability to confuse the enemy party, a missile attack or an instant kill ability against non bosses. There are also Magitek soldiers. Created by sucking the life out of Espers( The summon monsters of the game) and infusing it into humans. The two female main protagonists Terra (the half-esper) and Celes are examples. They will gain magic without needing magicite (Esper corpses,including Terra's father). The primary antagonist Kefka also went through the process and came out mentally insane because of it. Gau can also use Magitek from certain enemies but their abilities are not useful unless the player knows what they do before hand.
- Harry Turtledove's "Darkness" series is an Alternate History/Low Fantasy hybrid series of books concerning an analogue to World War II being fought by civilizations wielding industrialized magic; D&D style energy-throwing "sticks" as guns, dragons carrying alchemy-filled "eggs" as fighter jets and fighter-bombers, enormous rhino-like "Behemoths" as tanks, sea-serpent-like "Leviathans" as submarines, and so forth.
- The Escaflowne anime is famous for its Guymelefs, giant mecha consisting of giant armor suits with clockwork innards powered by the crystalline hearts of dragons.
- Harry Dresden, being a archetypical urban fantasy setting, has lots of examples of magic enchantments being applied to standard technology.
- Same thing happens in Harry Potter as well.
- The Discworld setting makes at least some use of the industrialized magic variety; the most prominent examples are the cameras, which use little imps to paint pictures instead of photoreactive chemicals, and a magical supercomputer named HEX.
- The Iron Dragon's Daughter is a very dark faerie-tale themed fantasy setting using industrialized magic. For example, as the title suggests, dragons are clockwork-bodied monsters built by elves as their equivalent to fighter jets.