I really liked the early kairosoft game like Game Dev Story, Grand Prix story, Pocket clothier etc Used to buy everything they made on it's launch but I stopped when they started following the DLC/Freemium trend, actually haven't bought any mobile games for a long time now.
Little Inferno. Went in, easy to grasp, just long enough to not be annoying while still satisfying, story was just present enough to engage. Amazing sounds, controls, visuals. A perfect experience. Runner up? I've played the hell out of every Infinity Blade and the series will always be on every ipad I ever own.
Port - KOTOR Made for mobile - Infinity Blade series, Battleheart Legacy, Oceanhorn, Crescent Moon RPGs, Orc Vengeance (no longer available)
Space Miner https://itunes.apple.com/nz/app/space-miner-platinum-edition/id353853276?mt=8 The link is for the platinum version, but I played the original version (TA Game of the Year 2010)
See signature I've been waiting for over 20 years for a Master of Magic remake/sequel/successor, and Planar Conquest is exactly that. Nimian Legends:Brightridge is the most lush and beautiful environment I have ever seen in over 30 years of gaming.
OK, I'll bite. The best game I've ever played on mobile is The World Ends With You. It looks great, sounds even better, has a good story and the mechanics of combat are really satisfying and brilliantly redesigned for a single touchscreen. Might be the best game I've ever played on any platform. For mobile originals, I guess Crashlands, Teeny Titans, Goblin Sword or Sky Force Reloaded.
I second Sky Force Reloaded, I still play the heck out of that game, and it's prequel before Reloaded got released. Also, X-COM: Enemy Within, I finished that game twice, which I seldom do with any game on iOS. Okay, it's a port, not an original iOS game, but still. Also a port, and a very recent one is Binding of Isaac, which have had me in a frenzy of gaming since it's release.
Monument Valley, Superbrothers: Sword & Sorcery, and World of Goo. Actually I played WoG first on the mac
Rayman Jungle Run if I had to pick just one, but it's a toss up including Infinity Blade, Monument Valley, The Room, Super Mario Run and Joe Danger. Notable mentions are the Cut the rope and Where's my water series.
Might and Magic The game that i like is Might and Magic from Gameloft it was a Java game but they made it so well It was the first in de serie the follow up wasn't that great but still a nice game you had several characters that you need to use to solve puzzles a vampire that could change in a wolf/bat/en mist an other character used bow an a chain to swing over gaps there was a guy with a big sword to fight with that could throw fireballs en throw storms real great.
No Bastion, Machinarium? I guess it's because they're also on PC but I do find Bastion's touch controls enjoyable.