You might have to erase data if you plan on using Amiibos with multiple games.
Amiibo games that require the ability to both write and read data on an Amiibo figure will have to erase data on a previous game in order to be used again, according to Nintendo of Japan.
For example, Super Smash Bros. for Wii U requires writing and reading save data on each figure. If you take these to games such as Hyrule Warriors or Mario Kart 8, the save data can be retained as these are read-only titles. If you use the figurines with both Smash Bros. and another game that requires writing save data, you might have to erase older data in order to make room for the new game.
Nintendo has not commented further regarding save data for Amiibo figures.