I haven't really tried out the PSX emulator for Wii. The PC Engine emulator works quite well, and the Saturn emu works about as well as can be expected given the Wii's specs and the state of Saturn emulation on non-PC platforms (read: more or less complete but very slow), but I don't actually have any PlayStation discs to try. All the PSX games I currently have are PSN downloads.
The systems I have tried are as follows:
-NES (FCEU GX): VERY complete and mature emulator. Part of a set of "GX" emulators that have a very professional menu system and unified features/interface, automatically check for updates, have robust feature sets including custom optional control settings to match Wii entries of various series, etc. Emulator is full speed with very good compatibility.
-SNES: Pretty much the same as NES. Frame rate drops slightly if you turn on smoothing (i.e. HQ2X), but if you stick with unfiltered or simple bilinear filtering, everything is full speed, even SuperFX games. Very good compatibility.
- GBA: Pretty much the same as NES and SNES. GBA emulation isn't *quite* full speed, but the only noticeable impact in most games is minor frame dropping. Definitely very playable, and feature set--like the rest of the "GX" emulators--is very mature and polished. Also supports Gameboy Player features such as rumble (if using 'Cube pad or Wiimote) and GameCube screen borders, as well as Gameboy/Gameboy Color/Super Gameboy features.
- Genesis: Similar level of maturity to NES and SNES, with good compatibility and robust features. However, the UI is different from the SNES/NES/GBA emulators, and allows a little more hardware-level tweaking (i.e. FM timing) but isn't quite as dummy-friendly. For example, the GX emulators mentioned above all let you set a "primary" control scheme, but if the primary controller (i.e. Classic Controller or GC pad) isn't plugged in, you can still use any other controller that *is* plugged in and it'll automatically default to that for controls. Genesis emu actually has to have correct controller set. Again, though, compatibility is very high, emulator runs at full speed, and also supports SMS/GG emulation at a similar quality level.
- SMS/GG: (see Genesis emulator)
- PC Engine: not as polished as the emulators above, but the actual emulation itself is still full speed with high compatibility. Does everything it needs to; just isn't quite as elegant as the others.
- N64: meh. Some things work, others don't. Like PC Engine, the interface isn't quite as polished as the GX emulators, and compatibility is a mixed bag. Some games have weird graphical glitches, and not everything runs full speed.
- Saturn: latest version of the emulator has good compatibility and fixes lots of graphical issues, but isn't really playable due to speed. Some 2D titles may run at playable speeds, but 3D games (such as NiGHTS) aren't really worth playing. My understanding is that--like many console Saturn emulators--the graphics are all software-rendered, which is part of why it's so slow.
- ScummVM: very mature, behaves pretty much like ScummVM on any other platform. The Wiimote is probably my favorite interface for playing these point-and-click adventure games, period.
- Virtual Boy: surprisingly decent. Compatibility is good but not perfect, speed is not quite full but certainly playable (about comparable to GBA), and yes it DOES have options for both 2D display and 3D glasses.
- WiiMC: not technicaly an emulator but still deserves a mention. Turns the Wii into a surprisingly capable media console. Doesn't really approach PC applications (or XBMC variants) in terms of library management, but playback is pretty good. Has integrated support for local storage, network storage, and streaming media (including a built-in YouTube search), and the DVD player works quite well.
There are plenty of other platforms emulated on the Wii as well, but these are the ones I've tried. Haven't really fiddled with Atari, Amiga, ColecoVision, Vectrex, arcade, MSX, NeoGeo, DOSbox, or any of the numerous others, so I can't speak to them--though I've heard most of these are pretty mature as well.
Prominent systems that are *not* emulated (to my knowledge) are anything after the N64 (duh), as well as the Genesis add-ons (SegaCD, 32x).
There's also quite a bit of good homebrew, including some titles that have since gone on to be released commercially in the iOS App Store.