This is a peculiar question which I have always wondered about, despite being absolutely useless to know.

How is it that the VC games run on the 3DS? (or VC on the Wii, for that matter)

In the case of a Gameboy game, does the 3DS itself have an emulator coded in to it? Or does each Gameboy game file have the emulator coding in it? Or, the final option I can think of, are Gameboy games 'ported' or recoded to run directly on the 3DS? Does that even make sense, or am I just babbling about technology I barely understand...

Surely someone out there knows the answer to this!

I'm not sure but my guess is that the 3DS has an emulator built into it. Seems more efficient to me at least.

Well, the 3DS doesn't have hardware emulation of the other consoles built in, that is for certain, which means it is emulating it via software.

It is possible that the firmware has a generic emulator built in that just runs the different game images, but I think this is unlikely. It is more likely that each game contains the emulator code because it is pretty hard to write an emulator that will run all games perfectly. They would all be based around the same "core", but any minor modifications required for an individual title could be made.

Having a single emulator built into the firmware would likely cause issue where changes needed for one game would break other games so every time a modification to the emulator code is made, they'd have to re-test every previously released game fully to ensure no problems. More work than it is worth.

On a side note, the 3DS emulates the DS(i) in hardware. Despite the hardware appearing to be similar, there are a lot of internal differences and it has to switch to "DS emulation mode" when running DS(i) games, hence why the home menu and sleep mode stop working. Also, I think some of the emulators use the DS hardware mode as the DS hardware is a better fit for how the graphics of the older systems worked, but I could be wrong on that one.

Yeah what DiggerDan said. The VC games on Wii and 3DS have emulators built into the download as far as I know. That's why the game files are so big, that and the manual.

Each VC game comes bundled with the emulator that runs it.

On this note, how good is the emulation?

I know that emulators written by the community have a hard time achieving perfect emulation - often some timing is off, or some graphical effect doesn't work properly. In fact, there is only one SNES emulator I know of that claims perfect emulation of every official SNES game ever made, and that's required lots of hard work and expensive research, for which it was lucky the author had contacts in the relevant industries to make it feasible.

Are Nintendo themselves able to emulate games on their hardware with zero problems, or are their VC game simply 'close enough' to the originals that most people won't notice?

We're getting close to the line between what's kosher and what's not as per our Rules. Please tread carefully, everyone :3

That said, in my experience with Wii VC titles, these are perfect emulations — there's slowdown, graphical glitchery, and other quirks in all these games i used to play when i was little, and they're all in the right places to boot. I'm not so sure with 3DS VC stuff (because I don't own much), but in terms of Wii VC stuff, it's pretty damn spot-on if you ask me.

OK, cool - one would hope that Nintendo could do a better job of emulating their own hardware than someone who's doing it as a hobby, but you never know!