Speaking of, I need a Splatoon mate, you up for some matches? NNID: teeqzter

Since everyone has already mentioned the obvious retail games, I'll skip those, although I'll echo the people who recommended LEGO City Undercover. I loved it, but be prepared for really, really... really long load times, like 30 seconds. Once the open world loads, though, it's incredibly seamless to move through the entire map, which isn't small.

From the eShop:
If you like puzzle platformers: Trine/Trine 2 (more adventure like) or Toki Tori (more straight up puzzling)
If you like twin stick shooters: Nano Assault Neo, and look out for RIVE this year
I don't have it yet, but from what I've seen of Affordable Space Adventures, it looks awesome. Same with The Fall.
If you played/enjoyed Puzzle Quest, Lucadian Chronicles is like a light version with card battles instead of match 3. It's free to play a large portion of it before you decide to pay for anything.

Since most of the good games have been listed I'll list the three games that were so disappointing that I sold (which I hardly ever do):

1. Hyrule Warriors: Too much grinding. All regular allies and enemies (the weak guys) just stand there, they don't even fight. And you can just sprint past them. The strategy element of the game is very simple and boring as well. Capturing bases seemed like it would be fun before I played it but it just didn't do anything for me. Basically in this game you just lock onto the beefier enemies and spam the same combos. Each boss is fun once then they are extremely repetitive. The plot is terrible. The game was too short (unless you liked the repetitive and grindiness of it). The voice acting for the characters was pretty bad as well (the anime grunts idk how else to describe it). I think this game would've been received much worse if it wasn't Zelda themed. If you want outstanding action/hack and slash games get Bayonetta 1+2 which are packaged together.

2. The Last Story: Terrible combat, poor controls, boring plot, okay characters (some good some bad). It has pretty bad performance issues as well, constant framrate drops. The game was a bit short as well. Overall extremely disappointed in this one. Just get Xenoblade Chronicles for an amazing RPG, that game blew my mind, everything about it was amazing.

3. Kirby's Epic Yarn: Good controls and artstyle but just really boring. No challenge, enemies weren't interesting (can't even remember the bosses even though I beat the game), the storyteller in the game talks to you like you're 5 years old. Don't think the music was very good because I can't remember that either. The transformations that Kirby can do were okay. Get Donkey Kong Country: Tropical Freeze for 2D platforming perfection. The New Super Mario Bros U/Luigi U games are excellent too.

A couple of other excellent games that you should look into are Super Paper Mario (don't let the haters say otherwise just because they miss the turn based combat from the previous entry on the GameCube) and Earthbound (unforgettable). 

*Essential when all the content arrives.

You have to get The Wonderful 101 and Bayonetta 2. Those are musts. You can try out the demo of both of them from the eShop. Fair warning though, The Wonderful 101 takes a bit to get used to. Once you do get used to it though, it's WONDERFUL.
(Plus, on Amazon Bayonetta 2 is only like $44 and it has two games, and you can find The Wonderful 101 at any retail store for $30 new)
Have fun with your Wii U! :D

And my NNID is Jaekization

Wii U? Well, you could preorder Project CARS for NX. O-)

You're not the only one who somehow managed to miss half the good games on a system owned by everyone and their grandmother (literally :P).  I didn't either Mario Galaxy, Metroid Prime Trilogy, I didn't even know Xenoblade Chronicles until almost a year after release when I was bored and looking stuff up.  It's a weird thing about the Wii, lots of good games half the people around didn't know about because of the whole casuals reputation. 

Ill add you later.

I knew you had good taste! :p

A copy of Bayonetta 2 just showed up at one of my local game stores and disappeared before I got to buy it.