SD cards are very popular for this purpose, because they only need a few pins (using SPI mode), and can be driven with simple “bit-bashed” SPI serial communications protocol, using free device drivers readily available on the Internet.
Until now, the big holdup for using an SD card in many homebrew projects has been the fact that SD sockets are not available at your local store, are not cheap (especially after shipping), and require ordering and waiting for them to arrive. But wait no longer! You can do it now! If not just laying around, or inside an old unused computer, you may have a spare connector inside the computer you are reading this with right now.