According to all legal precedents, emulation is legal within the United States. ... So in the US, emulation is legal but downloading a copyrighted ROM from a random website is illegal. If you want to emulate with the maximum amount of legality, you'll have to dump your own ROMs directly from your cartridges.
Yes and no. ROMs, like Hellfire Taco said, are illegal, but not the emulator itself. However, it is possible to play Pokémon games on a computer legally. You need to “dump” the game from a 3ds to a computer. Download a dumping software and use that to move the game files to your computer. As long as you don’t download games from the internet, own a dumping software, and move the game to your computer yourself, it is legal.
Source: The quote above, and I talked to somebody knowledgeable about this a while ago.