I second PictoParty! It might not be available to download on the store, but it's amazing. Using JNUSTool, it's still possible to download it onto your Wii U. : ) Also, it's available on Android (with use of Google Chromecast to show on TV), which I've done as well!
Some of my personal favourites (hopefully the not-obvious ones) I've found so far...
1)
Affordable Space Adventures uses the Gamepad, along with two Wiimotes with nunchucks to play a kind of Star Trek-y Captain's Chair game where you manage resources (switching energy, turning on and off lights & motor) through a control panel on your Gamepad. Best co-op experience, seriously, so engrossing.
2)
Spin the Bottle: Bumpie's Party uses the Gamepad & four Wiimotes to perform hilarious & inventive party games. (One of the Gamepad games forces you & a partner not to smile on the camera, while both the game itself & all your friends try to make you laugh.)
3)
Wii Party U-- why isn't anyone talking about this game?! It just packs SO MUCH GOODNESS. In my opinion, it's like a Mario Party & Nintendo Land hybrid. It DEFINITELY did a Mario Party style game better than Mario Party 10. Great gamepad ideas-- there's one that uses the gyroscope in the gamepad to make you walk over to scoop up water from a stream & carry it carefully back to your pitcher, there's this really cool circle dancing one where you place the gamepad in the center of the screen & create a sort of Wiimote chain, a sort of Newlywed Game one that plays like Ubisoft's cancelled Know Your Friends game, a game where you use the Gamepad's gyroscope & describe your surroundings to other players so they can locate you, even a really cool spin on a Pictionary game in it! Perhaps my favourite is this hilarious Twister-esque game where you have to all gather around three Wiimotes & the gamepad & hold down/release buttons.
4)
Game & Wario has absolutely wonderful single-player and multi-player game nuggets. I mean, why wouldn't Wario use a Gamepad the right way? WarioWare Touched! is one of the best DS games, after all! And before that, Twisted was one of the most amazing uses of the GBA gyroscope! Just like PictoParty & Wii Party U mentioned before, this game has Pictionary, as well, and
some people have figured out how to hack it to make it a more replayable experience. There's a really cool game where two people hold opposite ends of the Gamepad and tap touch-screen buttons to a beat that the other player then has to correctly mimic, like an instant Stepmania/DDR duel. There's also a strangely compelling game that's a bit like the Luigi's Mansion game from Nintendo Land where you have to figure out, from a huge crowd of randomly generated people, who's secretly the thief playing on the Gamepad.
5)
Typoman uses the Gamepad to solve cryptic word-based puzzles as well as provide you with really interesting clues along the way-- it really enriches the experience when you're playing and you suddenly get a little message on the gamepad to open up and read.
6)
Use Your Words uses the Gamepad/mobile devices/computers/etc. to participate in an Apples to Apples kind of game, except you get to write your own punchlines. Seriously, one of the funniest/funnest games I've ever played. (And, of course, if you enjoy Use Your Words,
check out everything at Jackbox Games, but that goes without being said!)
7)
6180 the moon uses the Gamepad for infinite two-screen platforming, where you're jumping/falling back and forth between the screens.
8)
Stick It To The Man! is -- okay, if you're looking at screenshots and think the characters look ugly, so did I. But I'm in 100% love with the game, without reservation, now that I've actually played it. At first, you might find it kind of odd that the touchpad controls of the grabbing hand are only used in off-TV play, but then when you get into the real game, there's this amazing twist to things where you read people's minds with the Gamepad in on-TV play. You hold the gamepad flat while you're walking around, and then when you want to read a mind, you rotate it so it's parallel with the TV screen. Then it's like if you had to Splatoon gyroscope, but instead of shooting, you're aiming at brains to listen to. (Their thoughts are played on the speaker of the Gamepad only, and the volume of the voices is responsive to how close you are to them, it's so cool!!) The writing is so sharp; it's by the guy who does
Dinosaur Comics. It's the first game I've played where it really, honestly feels like a platformer/point-and-click-adventure. Like, both. At the same time.
9)
Rayman Legends -- so, there's all the ports of it that are just fine and dandy, but the GAMEPAD ASYNCHRONOUS MULTIPLAYER is SO rad on this one. It really adds this feeling of cooperation due to having different skills. You can choose to play Murfy and throw bad guys off-guard by making them laugh, or moving platforms, cutting ropes, throwing things on slingshots, and using the gyroscope to turn giant wheels (which makes your teammates into, like, giant sentient marbles in a marble maze, yeeuh).
10)
Taiko no Tatsujin: Wii U Version, Taiko no Tatsujin: Tokumori!, & Taiko no Tatsujin: Atsumete ☆ Tomodachi Daisakusen! are a Japanese-only trilogy of rhythm games on the Wii U that all are compatible with the Wii U gamepad to drum on. Probably the only game series ever to make you look around for TWO Nintendo styluses. Endlessly appealing, shame they weren't translated-- though they are relatively intuitive! (All the same, thank goodness the Switch has been picking up the slack there.)
11)
The Beggar's Ride uses both touch controls and motion controls super gracefully as you gain magical powers throughout the game-- really balances solid normal platforming with the puzzle-solving on the gamepad.
12)
Kirby and the Rainbow Curse is a multi-player version of Kirby Canvas Curse for the Wii U gamepad, with a delightful touch of Epic Yarn in it! You create elaborate paths for Kirby to follow-- you can also use the paintbrush line you draw to clear paths that might be blocked by water, clay buildup, etc. Deliciously tactile experience, and the ability to be helper Waddle-Dees is icing on the cake.
13)
The Swapper is a case of using the gamepad as a map as well as a way to read electronic messages you receive throughout the game. It might not seem like a very ingenious use of the Gamepad, but when you play it, it really heightens the reality of it all-- similarly to Affordable Space Adventures. It strikes a similar tone to it, even. (Or, like, The Fall, which is also an amazing Wii U game, though it doesn't really use the Gamepad for anything at all. I just love story-driven sci-fi experiences.)
14)
FreezeME is an indie, uhm... I think I'm going to call it "A Hat in Time Lite". It's not polished, but it keeps giving me the same weirdly specific feelings of wonderment I got when I first played Super Mario 64. So, uh. There's gotta be something to it. The unique mechanic here is using the Wii U gamepad to take a picture of any object and freeze it in time.
15)
Tengami might seem like just a point-and-click at first, but it's actually more complicated than that-- it's a point-and-FLIP. There's plenty of puzzles in this that involve very deliberate flipping, and it feels SUPER good on a gamepad. Short experience that can be easily finished in an hour or so, but it felt satisfying to me. This one is also available for mobile!
16)
Chasing Aurora has excellent asynchronous gameplay by using the gamepad to have you play flying hide-and-seek & freeze tag games with the other players-- after every round, the game tells you to pass the gamepad to someone else.
17)
Puddle uses the gyroscope in the Gamepad to tilt fluid through an obstacle course-- SUPER fun-- if you've ever played Fluidity on WiiWare, this is like a continuation!
18)
The Bridge also is about tilting the Gamepad, but instead of being purely motion, you navigate a character through increasingly complicated MC Escher landscapes, with storytelling throughout akin to Braid. (Also, it has a rewind function like Braid!!
HYEE.)
(LIST LAST EDITED 07/02/2021)
Also, just going to second what's already been said about the Nintendo DS Virtual Console feature. Not only that, but the amount of injects possible are legendary. Like, if you're trying to play a Nintendo DS game and involve the rest of your friends or family in on it, there's no better way to show the action to everybody than to share it on your TV while playing on the Gamepad. We just finished playing Ghost Trick: Phantom Detective that way in my fAmily, and BOY, it was amazing.
And as
@Escorpion mentioned, all the LEGO series benefit from the gamepad in myriad ways-- I'm especially fond of how you can choose to have one player have their screen on the TV and one player have their screen on the Gamepad. There's also quite a few excellent classic-style point-and-click games (Daedalic Entertainment's
Fire: Ungh's Quest, Tiny Thief (might be a Japan exclusive, but it's entirely done without dialogue in-game)) using the gamepad-- As an adventure game enthusiast, I feel like the Wii U is really ideal for that. Retroarch, c'mon, make your ScummVM port on Wii U run betterrr~