The good news is you might already have games you bought on iPhone or iPad that are already free to download again on Apple's new set-top box. But if you're looking for something new, here are some ideas. You can play these on the included Apple TV remote, but we'd strongly recommend investing in a compatible wireless controller, too.
Beat Sports
One of the few exclusive games for Apple TV, Harmonix' Beat Sports is like Wii Sports and a rhythm-music game fused together. It all centers around timing actions to the music with simple swats of the Apple TV remote or button presses. This isn't complicated stuff, but it's kid-friendly, fun, and makes good use of the Apple TV remote's motion controls.
Crossy Road
Crossy Road is fun. It's addictive. It's free. It's this generation's Frogger, and on the larger screen it looks beautiful. It's also a perfect remote-friendly one-button game (with some trackpad swiping). There's multiplayer action too, if an iPhone is connected to play alongside.
Geometry Wars 3: Dimensions
The best arcade-action game on Apple TV thus far works a lot better if you have a wireless game controller like the Steelseries Nimbus. Quick dual-stick action, lots of levels and beautiful retro-neon graphics look and play as well as they do on the Xbox One or PlayStation 4 versions.
Does Not Commute
At first, this looks like a drive-around-town sort of Grand Theft Auto adventure, but Does Not Commute is really an ingenious puzzle game. Drive each person across town in the same timeframe, creating weird traffic patterns as routes overlap. I can't explain this easily. Just trust me: play it. Also, it works well with Apple TV's packed-in remote.
Lumino City
A puzzler game with a papercraft vibe that won awards when it hit PCs last year, the arrival of Lumino City on mobile and Apple TV is a welcome early addition. Its great looks are reminiscent of the PlayStation 4 games Tearaway or LittleBigPlanet, and shows what the Apple TV can handle graphically.
Rayman Adventures
Rayman's previous iPhone games have looked great but been simplistic. Rayman Adventures is even more like a true console-style platform game, but still keeps its basic controls. Good for kids, and has a wacky sense of humor.
Alto's Adventure
Everyone loves Alto's Adventure, and while I haven't been as head-over-heels for this basic endless action game, it's a wonderful fit on Apple TV. Again, one-button controls do everything effortlessly. The large vistas fit a bigger screen. And you might even own it on iOS, so you can download it for free on Apple TV.
Oceanhorn
The closest thing to Legend of Zelda outside of buying a Nintendo system. Even though Oceanhorn, previously available on iPhone and iPad, is a lot more simplistic in design than Nintendo's best Zelda games, it has a large adventure and lots of things to do, and a dose of that console feel.
Offroad Legends 2
It's a simple race-big-trucks side-scrolling game you've probably seen before on mobile, but the physics are fun and the two-button controls do a good job tilting the bouncy monster trucks across ridiculous stunt obstacles. Quick-fix gaming, and addictive...and still a good fit on larger screens.
Flick Quarterback 16
Apple TV doesn't have Madden. Flick QB doesn't come close, but it's a weirdly entertaining throw-the-ball challenge with flick controls that make a lot of sense on the Apple TV remote. If you're a football fan, worth a couple of bucks.