One Piece is digital only for America, so that is also out... It does not have to be a new (just released) game, but the newer the better.

I might give it a try to digital in September when I become desperate, but right now I will try to avoid them.

I had no idea it was going to be a digital only release, I was looking forward to adding another disc to my collection with that game! Oh well, digital it is then.

I'll join.

Not sure which month, but it would have been in the Winter or Spring: Disney Infinity
June: I grabbed Zombi U

Those are the only two 3rd party games I have for my Wii U. Any recommendations?

Lego City Undercover, Deus Ex HR, Shovel Knight, Stick It To The Man, Rayman Legends, Splinter Cell Blacklist, Unepic, Guacamelee and Knytt Underground are all pretty good games. Look up some vids in the eshop for these titles.

I might be repeating some of the games suggested by cannonballZ, but is because they deserve a second recommendation... and since I don't know if you have other platforms or not, I might suggest some other games in which the Wii U version is pretty decent.

Disc based: Deus Ex: HR, Rayman Legends, Ducktales Remastered, Need for Speed Most Wanted U, Splinter Cell: Blacklist, Darksiders 2, Batman: Arkham City

Technically not third party but they count: Lego City Undercover, The Wonderful 101, Ninja Gaiden 3 (only if you like the genre)

Digital only: Shovel Knight, Unepic, Guacamelee, Scram Kitty and his Buddy on Rails, Child of Light

Out of thsoe, I alread own for the PC:

Deux Ex: HR, Darksiders 2, Batman Arkham City, Child of Light

I will generally get multiplatform games on the system with the highest graphical fidelity, which 99% of the time is PC. But if a Wii U version is just as good, or almost as good, my intention is to get it on that system when at all possible. Stuff like Shovel Knight, Unepic, and Guacamelee are probably not being held back by any Wii U shortcomings, so I can get those on that system. I know Child of Light is restricted to 720p on the U which is why I went PC. 

I've also been looking at Lego City and Wonderful 101.  I'll add them to my list.  Thanks!

If you have a PC, you will buy most of the third party games for it, specially if the graphical department is so important... that said if you have not finished Deus Ex or don't mind playing it again or have some extra cash lying around, give it a try to the Wii U version, the control integration, graphical update, included DLC and fixed boss battles make it worth it, everyone with a Wii U should buy that game, and you can find it very cheap right now on amazon.com and other stores.

I had bought Pushmo World since i never had a Pushmo game before. Cutest puzzle game I have ever played. Unfortunately money contraints cause me much distress when wanting to buy Wii U games. I'll have to invest in Darksiders 2 at some point though, since it's coming down in price heavily.   

Purchased One Piece Unlimited World Red from eshop.

Well, to be honest I don't know. My download got cut short due to a power outage and I haven't been able to get into the eshop to restart the download since about 4:00 pm. For some reason the download was corrupted when the power outage happened and the Wii U couldn't continue the download. 

Are you having problems connecting to the eshop as well? I have been trying to download this game all day.