Game Boy/Color games can be played using an emulator called
Goomba Color. You download your ROMs from wherever you download ROMs, package them all into a .gba file using the included application, and then run that as you would any other GBA game.
The same basic process holds true for NES games with
PocketNES (get the latest version
here, Master System and Game Gear (SMSAdvance), MSX (MSXAdvance), Colecovision (Cologne), PC-Engine (PCEAdvance), SNES (SNESAdvance), Watara Supervision (Wasabi), Neo Geo Pocket/Color (NGPAdvance) and WonderSwan Color (SwanAdvance), all available
here.
Understand that not all of these run smoothly or at all for most or any games; I've personally only used PocketNES, Goomba Color and NGPAdvance. The first two are excellent and run most games just fine; Goomba Color can even do fancy stuff like show Super Game Boy borders on compatible GBC games, like Link's Awakening DX.
By the way, this is a question about emulation, and rightly belongs on the
GBA - Emulation board. You might want to read
this sticky, which goes into a lot more detail and includes more emulators than I've listed here.
