Wii
Manufacturer: Nintendo / Release Date: 2006
Wii Emulation Guide for PC
Recommended emulators: Dolphin
For Wii emulation, we're going to simply use the excellent Dolphin. So there's a lot of overlap with Gamecube emulation ... the tricky part is the fact that the Wii uses a lot of wacky and unique controllers like the Wiimote and Balance Board.
Dolphin's actual emulation of Wii games is great, and it's pretty easy to deal with ... pretty much download the emulator and go without any extra steps. It's the emulation of these unique controllers by using other devices (such as the mouse/keyboard and gamepads) that is, uh ... problematic at best.
This is compounded by the fact that some relatively simple games that you think would work with basic gamepad controls will insist on not working that way, requiring you to use the infrared pointer or shaking just for basic functions like scrolling through a menu (and both these features are at least a little flaky at the best of times with Dolphin).
One possibility is just to use an actual Wiimote, which Dolphin supports. If your computer already has Bluetooth support you're probably all set to connect one up. If it doesn't (often the case), you can add it with an external adapter/dongle.
I couldn't tell you how well Dolphin interfaces with an actual Wiimote, though, because I don't have one. I'm a humble man who just wants to play simple games, and I made a Xbox gamepad work well enough for basic functions.
Doesn't have to be Xbox but you should have a decent two-stick gamepad that Windows & games tend to autodetect for this to work. You can simply map the IR pointer controls in Dolphin to the left stick. Responsiveness is a bit jumpy, but works just fine for navigating menus and such. You'd think a mouse would be ideal for this, but I tried that and it just didn't want to work right at all.
That's fine for WiiWare games and such. You can switch to a more straightforward "Classic Controller" config for games like Mega Man 9. But let's say you want to play something more complex, like Super Mario Galaxy. You'll need to do a little more detailed configuration to work the Wii's functions into the gamepad - here's a good tutorial specific for that game and those with similar controls.
That covers most of the library except for "motion plus" games. A handful of games require this special expansion device that is more sensitive in reading motion than the standard Wiimote is. The most notable ones are Skyward Sword, Wii Sports Resort and assorted golf and tennis games. The simple answer here is that Dolphin still isn't very good about emulating this device and it's probably best to just ignore these games for now. That said, some dedicated people have figured out ways to play Skyward Sword and such anyway, but expect all sorts of playing around with configurations and experimenting and probable serious levels of in-game jank if you want to try it.