Bootleg
The term Bootleg in gaming world, refers to the unlicensed games made for various with a first-party company approval. In the case of NES and Game Boy is Nintendo, for Master System and Mega Drive is Sega, Neo Geo is SNK, and so on.
Arcade bootlegs
Arcade bootlegs started in later 70's with the success of Space Invaders. Numerous hacks, some of them, unlicensed, are done without Taito knowing about them. Many of these, are for providing faster shots and colored aliens. This will going on by Galaxian, Pac-Man and Donkey Kong.
Some games, such as Zig Zag, runs on weaker hardware other than the OEM own arcade boards. Sometimes, they can feature sound different from the original game. For example, bootlegs of Donkey Kong 3 exists, but ran on Donkey Kong Jr. hardware. Other bootlegs feature music completely different from the original game, such as Final Crash, the bootleg version of Final Fight.
In 90's, Asian companies such as Comad, made games on arcade boards from other companies, but without authorization of them.
Nintendo systems
NES / Famicom bootlegs
The first Famicom bootleg ever existent is Super Maruo, though it was released and quickly removed from the stores in Japan. The game features Mario trying to do something terrible with the Princess in a Deviantart-like level.
Some Famicom bootlegs are reproduced without sound expansion, such as Shui Guan Pipe, a bootleg of Gimmick!.
FDS bootlegs
FDS are not much common in Japan, but companies such as Hacker International released various games with mature content, such as naked woman. Of course, Nintendo not liked this, but the company did not make anything against him.
Game Boy bootlegs
Game Boy bootlegs are very common, by many companies from the Famicom bootlegs fame, such as Sachen.
Game Boy Color bootlegs
Game Boy bootlegs are not common, but many are hacks of simple platformers, such as Sonic Adventure 7 and Digimon Adventure.
Due to the fact that Nintendo almost killed the GBC in order to give support to Game Boy Advance in 2001, some companies like Syntax released GBC bootlegs on form of GBA cartridges.
Sega systems
SG-1000 bootlegs
SG-1000 bootlegs are common in countries such as Taiwan, due to a clone of the SG-1000 II called Aaronix, released from the company of the same name. At least, Aaronix later became a licensee for Sega products in Taiwan, even releasing the Sega Mark III.
There are a possibility of SG-1000 games to be copied on cassette tapes or diskettes, for use in SC-3000 and SF-7000, but this is not confirmed.
Mark III / Master System bootlegs
Mark III bootlegs was common in Asia (excluding Japan), initially by releasing MSX1 games (many from Konami) on it. But much like the Famicom, Mark III games from Taiwan came from altered logos and copyrights.
In South Korea, Samsung was unable to stop the sales of bootleg games, which many are not only conversions of MSX1 games from Japan, but conversions of MSX1 Korean games. Companies such as Zemina and Clover released many of these. Later on, there are multi-game carts that included MSX or SG-1000 games, but ran on Gam*boy. As much like the Famicom multi-game carts, they contains repeated games.
Curiously, some MSX1 conversions such as Nemesis 2 and F-1 Spirit, which originally used the K051649 (SCC1) in their original form, are not present in the bootleg Gam*boy versions.
Sega Mega Drive / Genesis bootlegs
Mega Drive bootlegs are initially multi-game carts, containing 3 or 4 games. They was sold in East Asia and South America.
Chinese original bootlegs are started to come in mid-90's, from companies like Gamtec and Realtec.
Russia also started to release their own games in later 90's, continuing their production until mid-2010's.
In South Korea, the first Super Gam*Boy bootlegs was just multi-game carts containing SMS that didn't take much space in ROM (even ones released on Sega Card format). Later on, their bootlegs are just unofficial distribution of games that Samsung does not released in South Korea, such as Sonic Classics.
Game Gear bootlegs
GG bootlegs came from Taiwan and South Korea, and many of them are SMS games inside on the GG cartridge / PCB. Sega did it officially with the GG release of Castle of Illusion.
Much like the Gam*boy, there are original bootlegs such as Street Hero.
Mega-CD bootlegs
The Sega Mega-CD rarely seen bootlegs of other games, although some games form Good Deal Games sells unauthorized game ports and prototypes for Sega Mega-CD.
Other
The Pico, 32x and Sega Saturn does not have own bootlegs, but there are chances of a 32x cartridge be a reproduction.
SNK systems
Neo Geo MVS
There exists bootlegs of both MVS boards and cartridges. And even worse, there are unauthorized multi-game carts, holding almost the entire MVS game library on one cartridge.
Neo Geo AES / CD
Some Neo Geo MVS games was not released in both AES / CD formats, however, there are bootleg cartridges that enable the use of MVS in a AES system, by just cloning the MVS ROMs into a AES PCB and applying the configurations in PCB to make the game compatible with the AES system.
It's possible to copy Neo Geo CD games in a CD-R, although due to how the Neo Geo CD didn't sold very well compared to Sega Saturn and / or Sony PlayStation, it's almost non-existent to see proper Neo Geo CD bootlegs.