Game Boy emulation is far from perfect, as sound emulation is not always great, and different types of Game Boy hardware aren't always fully supported.

Rew Download from Zophar's Domain This is one of the best Game Boy emulators around. Rew runs in Windows and has support for Game Boy, Super GB, GBC, and any combination of these modes. Rew is one of the few emulators that runs the Japanese Oracle ROMs properly.
VisualBoy Advance Homepage This extremely cool Windows-based emulator will run any kind of Game Boy game, as well as Game Boy Advance ROMs. It has many options and is very easy to use.
VBALink Homepage This emulator is based off of Visual Boy Advance but has link support. For Zelda you need to get 1.7.2. Check it out.
NO$GMB Homepage One of the better emulators around. There is a DOS and a Windows version, both with a nice GUI. If you want to play Game Boy Color games for more than 5 minutes, though, you have to pay money to register.
NO$GBA Homepage

Link Cable Instructions
This emulator has had an interesting past. First it was sold like NO$GGM. Then because it was hacked and released it was discontinued to the public. Now it is offered as complete freeware. It is small, and not as feature rich as others. But it works and it currently the only emulator that has a working link feature!
VGB Homepage The DOS version of VGB runs many games perfectly, but there is no GUI and the emulator is not being updated anymore.
VGB (Win) Homepage The Windows version of VGB has more features, such as Game Boy Color support, but the demo has no sound or joystick support. The full version costs $35 to register.
DBOY Homepage Basically VGB (DOS) with Game Boy Color support.