Finally, some runners up that couldn't be excluded.
As I said way back at the start of the feature, the Wii has an incredible library of music and there are many soundtracks I didn't include. Both of the console's Kirby games had excellent music, as do the three Trauma Center series entries, Epic Mickey, Donkey Kong Barrel Blast, the list goes on. Still, there are a few tracks I couldn't resist showcasing here because of their sheer awesomeness.
Any songs listed here stand out for being particularly memorable within a certain game, particularly catchy despite coming from a game with an otherwise boring or nonexistent soundtrack, or simply rocked too hard not to include them despite their game not qualifying for my top 10 faves list. But I digress, here is my final collection:

Wii Shop Channel
When you think of the Wii Shop Channel, it's likely that you instantly think of the catchy little ditty that plays during your store browsing. This tune seems to happily chirp the message "fill up your cart at Nintendo Mart!". Coupled with the adorable 8-bit Mario download animations, this tune totally alleviated any frustration caused when your online transactions took a long time to finish downloading.
Disaster: Day of Crisis
Main Theme
For the majority of writing this feature, this game was actually going to be on the top 10 list. That theme music perfectly fits the over-the-top action of the storyline, and is one of the most epic pieces of game music I've heard in years.
But one song doesn't justify a placement in the top ten, and while the rest of the game's soundtrack is also great, it just doesn't stack up to that one track. Regardless, this song sure does get the adrenaline pumping. Doesn't it make you feel like taking on the world?
Metroid Prime 3
Title Screen/Intro
This one track was, to me, one of the greatest moments of Metroid Prime 3. The story had built up over the last two games and we had to wait until an entirely new Nintendo console to be able to find out the conclusion to the story. Finally, the third game was released, and practically hurling it like a frisbee into the Wii disc slot the moment I brought the game home, I was greeted by this Terminator-esque piece of music. Foreboding, determined and grand, the title screen music perfectly sets the scene for the climactic finale of the trilogy.
Rayman Origins
Land of the Livid Dead Medley
Rayman Origins was a great game, but to be honest, I can't really remember much about the soundtrack except that it had cartoony squirrel voices that would, at times, get very annoying. However, one particular stage had an incredibly cool, catchy theme and it was the hardest stage in the game, both to access and to complete. The Land of the Livid Dead's addictive music was cool enough to warrant the hours and hours of infuriating frustration required to reach it, paying tribute to Old West movie soundtracks like The Good, The Bad and The Ugly.
I've included both tracks from the stage in one track for you to listen to.
You can thank me later.
Zero: Tsukihami no Kamen (Fatal Frame 4: Mask of the Lunar Eclipse)
Hard Mode Ending - Zero no Choritsu by Tsuki Amano
This last one is a little obscure, I know. Fatal Frame is one of my favorite video games series of all time, and yet beyond the occasional ambient noise they have next to no music at all. Fortunately their ending themes are quite cool, especially if you like the occasional J-Pop song like I do.
This song was performed by famous Japanese singer Tsuki Amano. Like many game and anime themes, it was also featured in the country's pop charts at the time, and has been released on an album in Japan. It's out of print now and getting a little hard to find, but I wholeheartedly recommend searching for a physical copy if you have the means to do so.
Well there you have it. I've tried to cover a wide range of music from my favorite Wii soundtrack list, and I feel I've represented many different music genres and styles in my choices. I hope you enjoyed listening. If you liked this feature, please let me know in the talk back comments below, I may consider running similar features for other old consoles and handhelds in the future.