Nintendo NES Classic Edition is a small replica of Nintendo NES, both adapted to modern times with an HDMI output, and keeping with nostalgia thanks to connectors for original game controllers, and pre-loaded with 30 classic games.
If you planned to add your own games however, the lack of USB ports, micro SD card slot, or any other storage or network interface could make it impossible. But based on a recent photo tweeted by Peter Brown, senior review editor at GameSpot, there may be light out of the tunnel, as while the main storage device (4Gbit NAND flash) is soldered to the board, the main board is powered by Allwinner R16 quad core Cortex A7 processor with a Mali-400MP2, and it’s quite likely UART / serial console and/or FEL interfaces are exposed on the board, making it possible to hack the device and potentially load your own games.
The other side of the board would really help finding out whether the UART pins are indeed available where I marked them [Update: Correct. NES Classic Hacked, see comments section]. If so, it would still be quite inconvenient to hack the board, as you’d need to connect a USB to serial debug board (normally a couple of dollars) in order to access the terminal, and either copy/paste code, or transfer data to the board. If some of the other connectors are carrying USB signal, it might also be possible to do some hardware hacking to add USB ports.
Thanks to Zoobab for the tip.