You just google it, it's not hard. Googling "wii genesis" got me all the info I need because it takes me to the WiiBrew page.
Officially supported games are called Virtual Console and are sold in the Wii Shop Channel.
http://en.wikipedia.org/wiki/List_of_Virtual_Console_games_for_Wii_(North_America)
Supported platforms are NES, SNES, N64(21 titles), Genesis, Master System, TurboGrafx-16(and Super CD), Neo Geo, MSX, Arcade and Commodore 64(all games delisted). And Kirby's Dream Collection used the VC name for two Game Boy games.
Arcade games usually had the most featured emu, with things like fake scanlines, motion controls, display editing, etc.
90% of the VC titles support 240p, except N64 and is always up-rendered at 2x the original res.
Emulation quality is not intended to be perfect, you just need to know that the supported games work really well.
GC had a GBA emu for in-store demos that doesn't save and is low with compatibility but the games it runs are either always full speed or really close to it and audio never stutters. Running this emu with Nintendont pretty much removes all the slow downs.
Homebrew emulators are all ports of existing programs for PC, this means that they have high compatibility with games but they're not as efficient in speed. This is a problem generally for GBA, N64 and PSone games.
http://wiibrew.org/wiki/List_of_homebrew_emulators
There's a lot of supported platforms I'm not gonna say here. But Genesis Plus GX was originally a port but was fully adapted to the Wii's hardware and is supposed to be 100% accurate with Genesis, GG, MS, SG-1000 and Sega CD, it also has one of the best homebrew guis out there. It's also one of the few homebrew that lets the user pick what kind of hardware filtering will be used, etc.
There's another emu called RetroArch which supports Final Burn Alpha games and just about everything else. It's not very user friendly.
There are three ways of running GC games on a Wii via sd/usb.
Dios Mios, Devolution and Nintendont. (yeah, they all have super lame names)
-DM replaces the software bit that loads GC mode to mount from usb or sd but is still very limited.
-devo runs games in Wii mode.
-nin runs games in Wii mode.
They've all got a compatibility list so look into that.