Game Boy
The gameboy line is a series of handheld consoles made by Nintendo, this article intends to focus on the gameboy and gameboy color so for information on the Gameboy Advance see the article linked.
While the gameboy line is technically a handheld line there exist several official and unofficial methods by which to play gameboy titles on various Nintendo home consoles occasionally with enhanced features, see the wikipedia article on the super gameboy for more.
The GBA line of handhelds (save the GBA micro) have the capability to play GB(C) titles although the hardware required means emulation is required if a GBA cart is to be used (1).
(1) Some GBA carts, although none in the EZFlash line, can use a so called GB-Bridge whereby the GBA cart is effectively turned into a GB cart.
GBA code[edit]
Both the mono and the color versions of the gameboy are well emulated using the GBA.
Gameboy Mono[edit]
Goomba is the choice emulator here, you can obtain it from flubba's site, EZFlash 1/2 users there is a builder for the emulator contained within EZClient.
Gameboy color[edit]
As the Gameboy color is slightly more powerful than the gameboy mono it was long considered impossible to have a full speed GBC emulator on the GBA but then DWedit came along and altered Goomba to make Goomba color. You can obtain a copy here dwedit.org
Also have a look in the forums on the site for new test builds: dwedit.org forum link
DS code[edit]
The is one emulator called DS_GBC available although it is very early stage and far surpassed by the GBA code emulators:
homepage (only source available)
Some builds: dcemu link
PC code[edit]
Most emulators the do mono titles will also do color titles, the GBA emulator VBA does fairly good emualtion (have a look at kode54's builds). Some GB(C) specific emualors include: no$gmb Made by the same author as no$gba (one of the best GBA emulators as well as DS emulators).
Also have a look at a fairly outdated but comprehensive list of emulators at zophar's domain