There can be little doubt that the Nintendo Gameboy changed the face of gaming. Launched in 1989 it was a major step forward in portable gaming. Until then gamers only had the choice of the little LCD games like the Game and Watch that pretty much just bleeped. On an aside, these are extremely collectable now, some of the rarer ones selling for hundreds of pounds.
When it launched it sold it's first shipment of a million units within weeks. It shipped with the highly addictive game Tetris, and several titles were available at launch. Hundreds of other games soon followed, further driving it's success. Competitors entered the market soon after, in particular the Sega Game Gear and the Atari Lynx. These were both colour units as opposed to the Gameboy's monochrome screen, but they didn't have the same battery life and weren't as successful. The Gameboy stayed true to what it learned from the Game and Watch series, it's about the game play, not the technology, that makes games playable.
Following the original Gameboy, a range of different colours was released, based on the original monochrome model. A redesigned, slimmer version was released in 1996, but it was still based on the original model. It wasn't until 1998 when the Gameboy Colour was released, which was a big step forward and was in response to developers who wanted a more sophisticated system. The biggest difference was the colour screen, but the rest of the technology remained pretty much the same.
The Gameboy Advance launched in 2001 and was a major re-architecture of the Gameboy. The original 8-bit Z80 CPU was replaced with a 32-bit ARM processor, memory was increased and the screen resolution was improved. Nintendo repeated it's earlier process by releasing different case styles and colours. It wasn't quite as successful as the original Gameboy, only selling 81 million units by 2009.
To date, the original Gameboy line has sold over 118 million units worldwide. It was retired in the early 2000's when Nintendo released the DS, and now the 3DS (which is really good!). Even with all these advances, I don't think anything can beat the original Tetris on the Gameboy.