A lot of people have asked how to get MonoGame running on Raspberry Pi.
The easiest way to do it is to run Win10iot.
Unfortunately, the performance is crap. win10iot doesn't use the gpu on pi, so it runs totally in software. I read somewhere that this is because the gpu is optimized for opengl, but win10 runs on directx.
Fortunately, the next step up win10iot device DragonBoard is still relatively cheap ($75), and DOES support directx.
Here's a MonoGame project running on Raspberry Pi 3, Win10iot, running at 848:480 resolution (the LOWEST 16:9 aspect ratio available):
It only gets about 15-20 fps
Same exact project running on DragonBoard, Win10iot, 720p:
It's running a solid 60 fps
Raspberry Pi 3 = old & busted
DragonBoard 410c = new hotness