The main impact of Pokemon was that it was a game that highlighted the gameplay (not convenience, but actual gameplay) advantages a game could have by being on a handheld. It utilized the full potential of the link cable and showed that handheld gaming could be just as much a social experience as could consoles, if not more. Since then, Nintendo handhelds have consistently outsold Nintendo consoles. The handheld industry is now poised to disrupt the console industry to become the most mainstream gaming market.
If you look at Pokemon Gold/Silver/Crystal sales, it's shocking how much they sold relative to the number of Gameboy Colors sold. Combined, those three games sold around 30 million copies, while the GBC sold (I believe) 40-50 million systems. The popularity of handhelds due to the games undoubtededly brought much more developer support to the systems over the years. The fact that the PSP can sell well despite the record-breaking sales of the DS shows exactly how massive the industry has become in such a short time.
Besides this, Pokemon was full of small innovations, some of which were so unique and well-executed that most developers have been reluctant to try to use the ideas themselves. The concept of parallel goals that support each other was in particular a showcase of how masterful the execution was. Players could focus on exploration (to catch new Pokemon and/or just to search around for undiscovered locations), on progressing the storyline, on breeding Pokemon, or on the multiplayer aspects (trade and battling), and each aspect would actually work to the benefit of the others, building the sense of immense possibilities without having to feel like a useless, inconsequential gameplay feature is being shoved in your face. In fact, I suspect the shoddy attempts at "tacking on" features that sometimes feel irrelevant to the game are largely influenced by Pokemon's success at doing so.
God that was a long post. I guess it's because I have always been and always will be a handheld fanboy.... (the two current gen systems I own right now are the DS and PSP)
