Amiibo Tap: Nintendo's Greatest Bits will launch in North America and Europe on April 30th, and in Australia the next day. It will be free to download in the Wii U Nintendo eShop.
When an amiibo is placed on the Wii U Gamepad's NFC sensor, that amiibo unlocks one of thirty different NES or SNES games. The Game that each amiibo unlocks is random. For example, a Pikachu amiibo could unlock Super Mario Kart. The same amiibo can only unlock one game each though. Once you tap the amiibo on the Gamepad, you can tap it on the NFC sensor again to switch to a different scene, with nine scenes per game. But each scene has a time limit to how long you can play it, so you can't play the whole game for free.
Here is the announcement video: