I've written an (incomplete) 8086 emulator in C++ [1] as part of a bigger project [2]. This kind of thing is really fun to do and gives you a lot of insight of how CPUs work (as a black box, though).
This guy spent three years disassembling the Outrun arcade ROM, then 2 years re-implementing it in C++, then extending his engine with features like high fps and new game modes, and is now onto creating extender tools like track and time editors.
Along the way he found several new bugs and provides a fixed ROM which can be flashed to the arcade board. He's also got a project to develop an SoC which uses his engine to run an arcade cabinet, completely replacing the original board.
It's a phenomenal effort and an amazing blog to read back through.
[1] https://github.com/ggambetta/emulator-backed-remakes
[2] http://gabrielgambetta.com/remakes.html