Wiiware:

Cave Story (I've only just begun playing it and I have to say it's hard, but not too hard that I won't want to come back and complete it, to be fair though, it's great)

Dr.Mario Online Rx (while I disliked the N64 one because it just didn't feel right, I tried Dr. Mario Online Rx and I'm surprised to say it's better, I don't know why ,but it's actually better)

Tales of Monkey Island Chapter 1-4 (I'm soon to get the 5th one ,but from what I've played, I like it)

Mega Man 10 (just your basic old classic Mega Man game, kinda do hope that the mainstream series does change in gameplay somehow :/, still like it)

Virtual Console:

Kirby 64: The Crystal Shards (good platformer, nothing more to be said)

Paper Mario (Paper Mario in my opinion is a N64 classic, just download it, do it)

Super Mario RPG (this game is incredibly hard and challenging, ALMOST finished it ,but when my data got erased somehow....let's just say it's a long story )

Ristar (Ristar is a awesome platformer, what else can I say, DOWNLOAD IT!)

Post your collection if you want.

Mines a very small collection Since I've only now gotten into playing my Wii.

WiiWare
Tales of Monkey Island: Launch of the Screaming Narwhal
Megaman 9
Doctor Mario
Pokemon Ranch(If that counts)

Virtual Console
Breath of Fire 2
Legend of Zelda Ocarina of Time
Super Metroid
Paper Mario
Sin and Punishment
River City Ransom

Small stupid collection ftw

Oh boy, here we go...
Super Mario Kart
MegaMan 2
Kid Icarus
Sin and Punishment
Super Mario RPG
Super Street Fighter II
Kirby 64
Pokémon Snap
Bonanza Bros.
ToeJam and Earl
Super Mario Bros. 3
Yoshi's Story
Wave Race 64
Mario's Super Picross
Super Mario Bros.: The Lost Levels
Metroid
Castlevania
F-Zero X
Paper Mario
Zelda II
Super Mario Bros. 2
Comix Zone
Lylat Wars (StarFox 64)
Kirby's Adventure
Zelda: Ocarina Of Time
Mario Kart 64
Super Mario 64

Pokémon Rumble
MegaMan 9
My Pokémon Ranch

...And that's it!

WiiWare:
My Pokemon Ranch
Pokemon Rumble (demo)
Grill off with Ultra Hand!

Virtual Console:
None, more fun to play games on original system.

Virtual Console:

Donkey Kong (NES)
Pac-Man (NES)
Super Mario Bros. (NES)
Super Mario Bros. 3 (NES)
Kid Icarus (NES)
Metroid (NES)
Super Metroid (SNES)
Kirby 64: The Crystal Shards (N64)
Sin & Punishment (N64)
The Legend of Zelda: Ocarina of Time (N64)
The Legend of Zelda: Majora's Mask (N64)

WiiWare:

SBCG4AP Episode 1: Homestar Ruiner
SBCG4AP Episode 2: StrongBadia the Free
SBCG4AP Episode 3: Baddest of the Bands
SBCG4AP Episode 4: Dangeresque 3: The Criminal Projective
SBCG4AP Episode 5: 8-Bit is Enough
Grill-Off with Ultra Hand!
Phoenix Wright: Ace Attorney

Pokemon Rumble and Photo Dojo. That's it.

Wiiware:
UNO (Boring, not my purchase choice.)
Defend your castle
My Pokemon Ranch
Pokemon Rumble

Virtual console:
Pac-Man
Super Smash Bros.
Pokemon Snap
Super Mario Bros. 2
Sonic and Knuckles

Let's see...*opens up Wii Shop Channel*
BIT.TRIP BEAT
Cave Story
Donkey Kong Country
Dr. Mario Online Rx
Grill-Off with Ultra Hand!
Kirby 64: The Crystal Shards
Kirby's Adventure
LostWinds
Mega Man
Mega Man 2
Mega Man 3
Mega Man 9
Mega Man 10
Onslaught
Pokémon Rumble
Pulseman
Punch-Out!! Featuring Mr. Dream
River City Ransom
Secret Of Mana
Sin & Punishment
Star Fox 64
Star Parodier
Strong Bad Ep1: Homestar Ruiner
Super Mario Bros.
Super Mario Bros.: The Lost Levels
Super Mario Bros. 3
Super Mario RPG: Legend of the Seven Stars
Super Mario World
Super Metroid
Tetris Party
The Legend of Zelda
World Of Goo
Zombies Ate My Neighbors

Dr Mario
Defend Your Castle
My Pokemon Ranch

Thats all, I got bored of the Wii about years ago.

Hmm let's see... *boots up Wii*

Ice Climber
Super Mario Bros. 2: The Lost Levels
Super Mario Bros. 2
Super Mario Bros. 3
Urban Champion
Donkey Kong Country
Donkey Kong Country 2
Street Fighter 2: The World Warrior
Super Mario World
The Legend of Zelda: A Link to the Past
Sonic the Hedgehog
World of Goo
Paper Mario
Pokemon Rumble (Demo)
Defend Your Castle
Dr. Mario RX (garbage compared to the N64 one. Delayed reaction time and lack of many modes is very disappointing. Plus the Miis are not as charming as the old characters.)

Let's see...

Pokemon Rumble
Exitebike World Rally (Kind of boring to me)
UNO
Super Smash Bros.
Super Mario 64
Mario Kart 64
Super Mario World
Super Mario Kart
Kirby's Adventure
Sonic the Hedgehog 2

WiiWare:
Final Fantasy IV: The After Years (with all tales) (only get it if you played final fantasy IV if you did I recomend this)
Pokemon Ranch
Pokemon Rumble
Grill-off with Ultra Hand

Virtual Console:
The Legend of Zelda
The Legend of Zelda:Ocarina of Time
The Legend of Zelda: Majora's Mask (my favorite Zelda game)
The Legend of Zelda: A Link to the Past
Metroid
Super Metroid
Super Mario 64