Turn your bedside photo of Mario face down, because it's time to get hacking.

Aside from those horrible controller cords and the fact that it can't make coffee, the biggest downside of Nintendo's NES Classic Edition is the fact that it only includes 30 games. While that might sound like a generous number, one look at the console's greatest games reveals that quite a few classics didn't make the cut.
While some fans expected NES Classic Edition owners to find a way around the 30 game limitation at some point, most expected the discovered method to involve hardware manipulation, minor coding, and a blood sacrifice to whichever evil god is en vogue at the moment. As it turns out, you really just need a Super Mario Bros.save file.
Ok, the process is a bit more involved than that, but the basic method that forum user madmonkey first discovered does indeed begin with a simple save slot. From there, you will need to hook up your NES to a computer and use some programs to modify the console code and add custom ROMs to the system's game selection screen. It's not exactly point and click, but the detailed method can be found on this Reddit thread.
Alternatively, you could just download the program created by user hakchi2 (available via this thread) which does much of the modification legwork as detailed in this instruction video.
Before you jump at the chance to add River City Ransom to your NES Classic Edition's library, be aware that these methods do come with a couple of catches. Namely, there is a chance you can cause serious damage to both your PC and your NES Classic Edition if you are not very careful. There are also reports of these methods generating warnings regarding virus uploads, but there does seem to be some debate regarding whether or not those warnings are valid.
Those words of caution aside, there is no denying that the end result of these methods is quite impressive. The additional games are added organically to the console's title selection screen which certainly bolsters the appeal of Nintendo's all-in-one convenient console design.