This is going to sound snobby, but the main reason third parties stear clear of Nintendo is Nintendo just is on another level of quality compared to many third parties. Hence why they don't sell as much on Nintendo platforms. Sure, you could argue the strength of IPs has something to do with it, but these Nintendo IPs are successful for a reason - they are the faces of quality games that have poven to be enduring to Nintendo gamers and enabled them to be popular in the first place. Nintendo doesn't put some spell over its audience compelling them to buy their games. They're simply at a level of quality that translates to sales. 

What third parties need to do if they want to do well on Nintendo platforms is really look at the elements of Nintendo's games that sell, emulate those features, and create some great products for their consoles. Not just crappy rushed ports, not afterthoughts or spinoffs by devs' B teams, but fully-fledged, quality software that has great and enduring gameplay. As long as these devs really put their passion into making great software, I really do believe that their games will sell very well. After all, there were plenty of quality NES and SNES third parties titles that sold strongly. Why couldn't this happen again?

Because these are the very same platforms that completely alienated and humiliated 3rd parties with stringent rules and dictator policies that drove them onto other, more friendly and technically advanced alternatives where they found even more success.

What games did it get? I have a pretty solid Wii collection and I can only think of five good third party titles for it.

Which 5 and I might be able to expand on it.

Found a few more than 5 after doing some digging. This list isn't 100% complete but...

No More Heroes

No More Heroes 2

Monster Hunter Tri

Muramasa

Dead Space Extraction

Mad World

Little King's Story

Rayman Origins

Trauma Team

Trauma Center

Boom Blox

Boom Blox 2

Zack and Wiki

All in all that's around thirteen solid third party titles vs fifty or more on the other systems.

XBox/MS basically screwed Nintendo's third party support, once third parties had *two* more attractive options for their games instead of just Sony + Nintendo (by default as Sega wasn't getting much), Nintendo was always going to be like a third wheel.

Switch is a bit different in that it is opening the door to high powered portables it does open the door a little bit at least. I think developers have been attracted to the userbase that Nintendo can attract with portables but in the past their portables were so woefully behind any kind of modern game engine that you couldn't really make any of your modern games for a GBA or DS. But with Switch you can in a lot of cases.

It doesn't necessarily need the same amount to have decent third party support.

But beyond that:

Final Fantasy Crystal Bearers

Dragon Quest Swords

Pandora's Tower

The Last Story

Sin and Punishment

Red Steel 2

Sonic Colors (yeah, a good Sonic game)

Okami

Fragile Dreams

Tales Of Symphonia Dawn of The New World

Harvest Moon

Silent Hill Shattered Memories

Rune Factory Frontier

ect, ect, ect.

They had tons of great games. Not to mention the return of the on rails arcade shooters like Umbrella Chronicles, House of the Dead and leaving out Metroid Other M which was really made by Team Ninja.