This is one of the few strategy games that I've checked out for iOS. It's like a reverse version of the board game Pandemic. You control a virus, and get to help it evolve and spread throughout the world. You have to decide what you want the symptoms to be, how it spreads and so forth, all in reaction to the world around it. It's engaging, and a game doesn't take overly long to play.
9. GAME DEV STORY
If I remember correctly might have been the first game that I got for my iPod Touch. It's basically a sim game where you run a game development company. You hire programmers, artists, etc and make them work on whatever type of game you want. You have to decide what you consoles you want to work with, and how quickly you want to start working on them. It gets a bit repetitive later in the game, but the theme is so strong that I was drawn to it despite its flaws.
8. SUPER HEXAGON
One thing iOS really excels at is making games with really quick gameplay loops that are easy to learn, but tough to master. Super Hexagon is a zen level example of that genre. Basically all you do is try to rotate yourself through this shape maze, but it gets really tough, really quickly. It's one of those you really need to play to see what's special about it, because the gameplay is just about perfect.
7. HAUNTED HALLOW
This is interesting because it's essentially a board game created exclusively for a digital platform. It comes from Firaxis, who was responsible for the newest XCOM games, so it's got a really strong sense of strategy. You basically build a haunted house, then send monsters into the town to try to scare the villagers while your opponent does the same. There's a good amount of strategy to it in regards to the type of units you can build, and it's very fun throughout.
Endless runners are a huge deal on mobile devices, and this is one of the sharpest. You're an Indiana Jones type running through underground caves fighting off various monsters you encounter. The game has a ton of charm, and there's enough things for you to get to continuously upgrade your character as you play. It's quirky sense of humor really makes it easy to come back to over and over.
5. DEVICE 6
This is the type of game I was hoping existed when I started playing iOS games. It takes complete advantage of the system it plays on and wouldn't play the same in another form. The game is basically a text adventure, but that sells it short quite a bit. You scroll through the text of the story, and it acts like a maze you are navigating. Sometimes you pick with direction you go first, often causing you to flip the actual iPhone as you are doing so. There are also a good amount of visuals throughout. You progress through the game by solving puzzles, the kind of old school puzzles that you need a pen and paper to solve. I haven't finished the game, but it's an absolutely refreshing experience that reminds me of the first time I read House of Leaves.
4. RIDICULOUS FISHING
Another perfect gameplay loop type game. The game basically has three portions to each round. First, you cast your line and send your fishing hook down. While you are doing this, you try to dodge all the fish around you. Once you hit one, you start to reel it in. During this portion, you try to touch as many fish as you can to pull them up. And when your hook reaches the surface, they all get tossed up in the air. At this point, you have to shoot them out of the sky. It's massively entertaining, and there are enough things to buy in the game that make you get progressively better as you continue to play. It's an absolute blast to play.
3. JETPACK JOYRIDE
This is the endless runner to end all endless runners. You just keep going, trying to avoid all the traps in the facility by flying up and down the screen with your jetpack. There are also some really cool vehicles you can get that give you different advantages throughout. Again, with the money you earn while playing you can buy upgrades, both gameplay and cosmetic, to give the game more variety.
2. MIDDLE MANAGER OF JUSTICE
Another great sim game, this one coming from the good folks at Double Fine. Basically you are the guy who coordinates a Justice League type superhero team. You hire heroes, send them out to do heroic things, like saving a bus full of children or fighting off robbers. There are different sections of the city that you can progress through, each with a different villain storyline involved with them. It's a lot of fun, and the theme works perfectly in the game. I wish there was still some new content coming out for the game, as I tore through it all quickly.
1. KNIGHTS OF PEN AND PAPER +1 EDITION
This game is a fully developed RPG that plays out entirely on iOS. The theme is that you are a group of people playing D&D, and the battles you see play out are the story you guys are playing. It's one of the few iOS games that I've really paid attention to the story. The game progresses at a great pace, though it does ramp up quite a bit towards the end. The battle system is amazingly solid, and the amount of character combinations you can create is amazing. I can't stress enough how fun this game is, providing a wonderful old school RPG experience in such a small little package.
Honorable Mentions: Dead Space, Plants vs Zombies 2, Papa Sangre II, Organ Trail, Hearthstone, Republique