I've owned an Nvidia Shield for a little under a year now. The situation hasn't entirely changed: I use it most often as a portable emulator, and it's wonderful for that. I beat Mother 3, Drill Dozer, and Super Metroid a while back, and I'm working my way through Final Fantasy 6 now.
But there are more Android games that natively support physical controls now, especially as the Ouya and add-on joysticks have raised the profile for Android gaming. It's not a huge library, but between Humble Bundles and what's in the Google Play store, I certainly don't feel cheated. If you're thinking about picking one up, here's what's good (and what's merely playable) so far.
Aquaria may be the best value for the dollar on Shield, which makes it weird that apparently you can't buy it for Android anymore. A huge, sprawling Metroid-alike set underwater, with a beautifully-painted art style, it's the first game that I played where the Shield's controls not only worked, they worked really well (which figures, since it was developed for XBox controls alongside mouse and touch). If you managed to nab this in an old Humble Bundle, it's well worth the installation.
Actually the third in a series of "tower offense" games, where you send a small group of tanks through a path filled with obstacles, Anomaly 2 is one of the weird cases where the physical controls work, and are very well-tuned, but you still kind of wish the game was on a touchscreen. Playing the earlier Anomaly titles on a phone, you'd get into a groove of tapping icons to balance your resources, targeting, and path. It had a nice Google Maps fluidity to it, and that kind of speed suffers a little bit when panning around via thumbstick. It's still worth a look, but probably better played on a touch device.
In contrast, Badlands seems like a poor match for the Shield--it's a single-press game similar to any number of other smartphone titles (Flappy Bird, Tiny Wings, etc). But there's one distinguishing factor, which is that the triggers on the Shield (which are mapped to the "flap" action) are fully analog, so the harder you pull the faster the onscreen character flies. It's a small change, but it completely alters the feel of the game for the better. The layered, 2D art style is also gorgeous, and the sound design is beautiful, but on the other hand I actually have no idea what's going on, or why some little black blobby creature is trying to travel from left to right.
Most of these games come from the Humble Bundles, which are almost always worth throwing $5 at, but I actually bought Clarc from the Google Play store. It plays a bit like Sokoban, mixed with Portal 2's laser puzzles and Catherine's block/enemy entrapment. Previously released on Ouya, the controls are still solid on the Shield, and the puzzles follow a nice pattern of seeming impossible, then seeming obvious once they're worked out. A super-fast checkpoint system also helps. It's cute, funny, and good for about 6 hours of serious play.
I'm in favor of anything that puts Crazy Taxi on every platform in existence, but only if it's coded well. The problem is that while this port supports the gamepad, it's hamstrung by the adaptations made for phones — namely, the Crazy Drift can't be triggered manually, and the Crazy Dash feels sluggish. In a game where you need to be drifting or dashing almost all the time, this pretty much ruins your ability to run the map. I'd say to skip this unless it's on sale.
Gunman Clive was originally released on the PS Vita, and it shows: a cel-shaded platformer with a strong Contra influence, this is another bite-sized chunk of gameplay. It does seem to be missing some of the bonus features from the original release, but there's still plenty of variety (and some huge, fun bosses) to fight. Considering that it's only a couple of bucks, it's well worth the price if you're in the mood for some neo-retro shooting.
Speaking of retro, one of my favorite discoveries is the games that Orange Pixel has been tossing out for all kinds of platforms, particularly Gunslugs and Heroes of Loot. Both are procedurally-generated takes on classic games (Metal Slug and Gauntlet respectively) with a pixel-art design and a goofy sense of humor. The rogue-like randomization of the levels makes both of them compulsively playable, too. They're great time-wasters.
One of Gameloft's derivative mobile clones, NOVA 3 is trying very hard to either be Crysis or Halo. It doesn't really matter which since the result is just boring man-in-suit shooting, with sloppy, ill-configured thumbstick controls. All that, and it's still one of the more expensive titles in this list. Definitely skip this one.
Rochard was released on Steam a while back, and then re-released just for Shield this spring. It's a clever little puzzle-platformer that's based around a Half-Life gravity gun, but also some light combat. It would probably be better without the latter: the AI is generally terrible, and the weapons aren't inspiring. At its best, Rochard has you toggling low-gravity jumps, stacking crates, and juggling power cells to disable force fields, and those are the parts that make it worth playing.
Finally, fans of shooters have plenty of options (including remakes of R-Types I and II), but there's something to be said for time-travel epic Sine Mora. Although it makes no sense whatsoever, it's a great bullet-hell shmup with a strong emphasis on replayability through different ships and abilities, score attack modes, and boss fights. I love a good shooter, even if I'm terrible at them, and this is no exception.
What's missing from the games on Shield so far? I'd like to see more tactical options, a la Advance Wars or XCOM (which has a port, but doesn't understand gamepads). I'd appreciate a good RPG. And I'd love to see a real, serious shooter that's not a tossed-off Wolfenstein demake. But it's worth also understanding why these games don't exist: the economics of the mobile market don't support them. When your software sells for $5 a pop, maximum, you can't afford to do a lot of content development or design.
The result, except for ports from more sustainable platforms, is a bunch of quick hits instead of real investments. Almost all the games above, the ones that are worth playing at least, were either released on PC/console first, or simultaneously. The good news is that tools like Unity and Unreal Engine 4 promote simultaneous mobile/PC development. The bad news is that getting better games for mobile may mean cheapening development on the big platforms. If you thought that consoles were ruining PC game design before, wait until phones start to make an impact.