Nintendo's Game Boy handheld was first released in 1989. The gaming device was the brainchild of long-time Nintendo employee Gunpei Yokoi, who was the person behind the Ultra Hand, an expanding arm toy created and produced by Nintendo in 1970, long before Nintendo would enter the video game market. Yokoi was also responsible for the Game & Watch series of handhelds when Nintendo made the move from toys to video games.
When Yokoi designed the original Game Boy, he knew that to be successful, the system needed to be small, light, inexpensive, and durable, as well as have a varied, recognizable library of games upon its release. By following this simple mantra, the Game Boy line managed to gain a vast following despite technically superior alternatives which would have color graphics instead. This is also apparent in the name (conceived by Shigesato Itoi), which connotes a smaller "sidekick" companion to Nintendo's consoles.
Game Boy continues its success to this day and many at Nintendo have dedicated the handheld in Yokoi's memory. Game Boy celebrated its 15th anniversary in 2004, which nearly coincided with the 20-year anniversary of the original Nintendo Entertainment System (NES). To celebrate, Nintendo released the Classic NES Series and an NES controller-themed color scheme for the Game Boy Advance SP.
Boycott Advance was developed to run home brew Gameboy Advance software, and to that end it works quite well. It is also able to run a wide variety of commercial games, although there are some known issues that prevent some titles, particularly newer ones, from working correctly. You can download it from Richard Bannister's site.
KiGB sets new standards for emulator compatibility, with every single released GB and GBC title having been tested as perfectly compatible as of the latest release. Download from Richard Bannister's site.
VisualBoyAdvance is an emulator for Gameboy and GameboyAdvance systems. You can find more info and download at VBA Sourceforge page.
mGBA is a new Game Boy Advance emulator written in C. The project started in April 2013 with the goal of being fast enough to run on lower end hardware than other emulators support, without sacrificing accuracy or portability. Even in the initial version, games generally play without problems. Download it from mGBA downloads.