Between WiiWare, Wii retail and any old Virtual Console games just about every major genre is covered with some depth now on Wii. It really depends on the genres you like and what kind of depth you expect...
That said, NES / Genesis / TGFX 16/ SNES / N64 / Arcade / GC / WiiWare / and Wii games are all playable for Wii.
Personally, I think Wii is already the best system ever for platformers, so if you like that genre at all its really a good buy.
Off the top of my head for platformers you have all of these titles available by the end of 2010 that are good to excellent between WW, VC, and Wii retail:
Cave Story, MM9, MM10, Lost Winds 1-2, SMB 1-3, Lost Levels, Mario World, Kirby SNES, Kirby NES, Sonic 1-3, Sonic & Knuckles, Yoshi's Story, DK64, Metroid, Super Metroid, Sonic 4, And Yet it Moves, Tomena Samner, La Maluna, Muscle March, Bit.Trip.Beat, DKC 1-3, Donkey Kong arcade, Mario Bros, Max & the Magic Marker, Nyxquest, Robotz, Wario Land, Galaxy 1-2, DKC Returns, Kirby Epic Yarn, A Boy and His Blob, Nights, Epic Mickey, Jett Rockett, New Super Mario Bros. Wii, De Blob, Muramasa, Sonic & The Secret Rings, Sonic Colors, and there is probably other good stuff I'm missing.
Other than sports / fitness (Wii Sports, Wii Fit, Shaun White, WSR, Deca Sports 1-3, NBA Jam, Punch Out, We Ski, Tiger Woods, Madden, Mario Tennis VC, etc) Wii's strongest genre is probably platformers.
Shooters / RPGs are fairly well covered now even. You have Goldeneye, several COD games, Conduit, Metroid Prime 3 and a couple other strong shooters. Wii isn't shooter driven like PS3 / X360 but there are some real gems now. RPGs you have Shiren, Zelda, Monster Hunter 3, a Chocobo game, Tales, the sequel to FFIV, all the VC RPGs, and lesser stuff like Final Fantasy Crysal Chronicles Wii and then the eventual stuff like Last Story, DQX, Zelda: Skyward Sword.
There is surprising depth for what I would broadly call strategy games on Wii actually - Swords and Soldiers, FFCC: My Life as A Dark Lord / My Life as a King, Fire Emblem, Dawn of Discovery, Little King Story, in addition to VC stuff and upcoming games like Gods vs Humans (WW), Pikmin 3 (Wii) and a couple others I'd reckon.
The weakest Wii genre I'd say is racers. You have Mario Kart...some stuff on WW thats mediocre, some NFS games...and not much else.
So it really depends on what you like.