The games I own, in no particular order...
Mario Kart 8: Easily my favorite (and I think best) game on the console. In my opinion the greatest karting game ever made (including DKR, suckas) and I've owned most of them. It's so good I bought it once, beat it, had it stolen from me and bought it again. $120 and well worth the price. Plus they put out so much DLC for another $20 you get 6 playable characters, a few variants, and four completely new cups (that's 16 total tracks). I will literally not stop playing this game until Mario Kart 10 comes out (because 9 will be a handheld, like they always do).
DK: Tropical Freeze: I wasn't a big fan of DKC Returns on the Wii, but that's mostly because I hate the Wii with an ongodly passion. It's not quite as good as the originals (and nothing ever will be) but if you love the Donkey Kong Country series there's enough here to satisfy the itch.
Smash Bros: It's Smash Bros. Are you a human being?
Hyrule Warriors: I really like this game, without ever having sunk too much time into a Dynasty Warriors game, but that's basically what it is. The love and history for the Zelda franchise put into this game is amazing. It's super repetitive but it's also hella fun and never takes itself too seriously. I had a lot of fun with the story which is ridiculous, but the classic maps and DLC are what make it a must-play game IMO.
Nintendoland: A criminally underrated collection of mini-games. It was bundled in to teach people how to use the gamepad and its functionality in a fun way. Ironically it's still one of the only things that make the gamepad a thing that needs to exist.
Yoshi's Wooly World: I haven't played it yet. But I intend to when I'm doing with Dying Light and Bloodbourne on PS4.
Bayonetta 2: So fucking good. Did you like Bayonetta 1? Have you never played Bayonetta? PERFECT! Buy the physical edition and it COMES WITH THE FIRST GAME FOR FREE! This is one of the must-buy games on the console IMO if you like quick-paced action hack-and-slash games that maintain intelligence in its combat. Like a smart version of God of War, with more attractive boobs.
Other games that are good that I've played but don't own include:
-Captain Toad: If you love the puzzles in Super Mario 3D World get this game. It's really charming and a lot of fun. It's also only $40 new.
-Wonderful 101: Super fun game. I want to pick it up but there's so many games on my list right now that I already own.
-Splatoon: I was really excited for this game, but I'm glad I didn't buy on day one. It's fun. I had fun with it. But I'm not obsessed with it, and the one-dimensional game mode really limits how much replay value I will probably find with it. But other people really like it, and you might too. It's just not a thing I want to sink time into.
Also if you haven't played Windwaker or want to revisit the game, the HD version is the best way to play it. Gamepad support is tight. The Mario games are all fun. I probably won't buy another Wii U game until Xenoblade Chronicles X. I think that's going to be one of the best, most deep games on the console and a must-own even if you aren't familiar with the series.
OH, a few third party games I own too. Ducktales Remastered is a lot of fun. Steamworld Dig. Shovel Knight (I have it for 4 different platforms, because it's just that god damn good).
So yeah. Anyone who says the Wii U doesn't have any games can suck it. Also do yourself a favor and buy a Pro Controller. You will thank me.