Pretty hard to chose only one game. Even with the dumb mentality that spreaded around about the Wii only having "shovelware", there's actually a lot of good stuff to enjoy.
Ignoring Nintendo developed games for the sake of variety (and because of course Nintendo games are going to be some of the best for their own consoles), it also had quite a few very solid 3rd party games.
Red Steel 2 is still one of the better games made by Ubisoft in my mind. While the plot is thinner than the first game, everything else is so, so much better. Gameplay is phenomenal, the motion controls always worked well for me, and there's a lot of moves you can do between normal attacks, special moves and mystical arts, you can combo them in different ways too.
You can for example do an upwards slash to send an enemy flying, and then you can either take out a gun and riddle it with bullets as it falls or jump towards him and start slashing, and then you can just keep slashing as you both fall, or you can slam him to the ground, and then you can either shoot at him as you fall, or take out your sword and impale him.
This is one example, but there are many other ways to fight enemies, and the game never gets boring. There's also lots of upgrades and improvements you can do to your character and equipment, so you're always trying stuff. Between that and the smooth 60 FPS games and stylized visuals, the devs really did a great job with it, and I'm so glad I gave it a chance.
Geometry War Galaxies is another game I spent way too many hours playing to this day. It's a Vectrex inspired, twin-stick Shoot'em Up focused on doing High Scores. Originally it appeared on Xbox 360, but this is an expanded and more complete version.
You're put in a limited area in which you can move around, and enemies, which are also geometrical formations, spawn all across the field (and sometimes outside). It's all about reflexes and strategy, as each enemy type has its own behavior and if you don't pay attention you can screw up easily, and each stage ramps up difficulty as time goes on. One great thing they added for this are Drones. These little guys can be bought with points you accumulate by playing well, and they can have a multitude of modes with different abilities, and each one can level up to become smarter, faster and more powerful.
While the visuals initially look very simple, once the game starts to take off, it becomes a light spectacle, full of neon lights, explosions and chaos. To me it's one of the best looking games of its generation just because of how mesmerizing it is to see a high-level play, specially since the game runs at 60 FPS smoothly, which is both great for the gameplay but also to make all the stuff moving on screen be more satisfying. It's a hard game, one that needs concentration, but daaamn if it isn't fun.
I mean check this screenshot (this is not even close to being the craziest the game gets):
I could talk for days about Wii games, but the last one I'll mention is
Opoona. This one take me off guard, and I ended up loving it. It's a very quirky and interesting RPG. You play as a kid alien that traveled with his family through space for some nice vacations when something goes wrong and crash lands on a planet unknown by him. Fortunately he's alive and also brought to one of the planet's domes, where people live. From here, the poor little guy has to tough up and try to find its family.
It's a really interesting game thematically, because it's about trying to adapt to a world and society that you know nothing about. Getting jobs and progressing through them, socializing, making friends and doing things with them, learning about the history of this world, exploring around and such are core parts of the game. If you like lore and world building, this game has it in spades. Heck, it has a TV you can watch with different programmings, from news, to sports, to tv shows and informative programs, you can even learn the planet's evolution of Art, and you can visit museums and see their art creations, which make you grow your non-battle stats that impact on how you speak with NPCs and such.
The game also has lots of commentary about modern society and human behavior, if you like to use your brain ever-so-slightly too. And then there's the RPG side, of course. The Battle System is pretty unique and fun, it's a mix of turn based with some real time inputs for attacking (and no, it's not button mashing, it's more fun and simple than that), and battles are pretty short and to the point, which makes the pace pretty good. There's equipment, spells to learn (here called Force), and it has a lot of interesting mechanics and systems. For example, exploring around cities (which are pretty big), there are little things attached to walls. Finding them is actually a game played in this world, and you receive points that can be exchanged for prices.
It's often compared to games such as Earthbound, and while I can see where they come from, being a quirky, very different feeling RPG compared to your usual stuff, they have very different personalities. Sometimes I feel I like it even more than Xenoblade Chronicles. I can just lose myself into the game whenever I replay it.
Oh, and the music is
AMAZING. It's the f****g best icing on an already tasty cake. The game is not for everybody (like if any game was...) and visually so simple it reminds me of a Dreamcast game (not in a bad way, mind you), but if it grabs you, you're going to have a great time. Another game I'm super glad to gave a chance.
...Anyway, those are three, and I'm not even scratching the surface of great memories with the Wii's library, there are so many more. Right now I'm replaying La-Mulana, a metroidvania for Wiiware (also on Steam), and what a blast from the past. Also, it's one of those games that loves making you mad, and I forgot how fun those can be in current gaming.