Non-violent games by non-evil companies, as recommended by my Twitter stream.
I've listed things with an "iOS > Mac > Other" bias, but many of these are available on other platforms. Use your least unfavorite search engine, or check the developers' sites, for different versions.
The Legend of Zelda: A Link To The Past by Nintendo is designated as the highest amount of artistic violence in a game and bad behavior in a company that is allowed on this list, given that both are considered by many to be the Greatest Of All Time.
Companies like Zynga, PopCap, and their parent company Electronic Arts, produce games that are often fun, but addictive and freemium-driven, at least on the App Store. What's wrong with freemium?
This list is meant to be an alternative to such games, if only because nobody has any trouble finding them. Similarly, I've not listed sport franchises or dynasties like Mario, because that would artifically dilute the list.
I may make provisional exceptions and list games people seem particularly passionate about, but I am often wrong, so if you disagree with something listed here, please file an issue, fork it, and issue a pull request.
Folks have recommended anything by the following lesser-known game makers. While not all their games may meet the criterion of non-violence, as companies, they seem to meet the standards.
- Beat Sneak Bandit by Simogo
- Bridge Constructor by Headup Games
- Carcassonne by TheCodingMonkeys
- Circadia by Simple Machine
- Clickomania by R2 Soft
- Coolson's Pocket Pack by Things Made Out Of Other Things
- Connectrode by Deep Plaid Games
- Contre Jour by Chillingo
- DEVICE 6 by Simogo
- Enigmo by Pangea Software
- Flight Control by Firemint
- Fling! by CandyCane
- Forever Drive By supermono limited
- Frenzic by Iconfactory
- Game Dev Story by Kairosoft
- geoDefense Swarm by Critical Thought Games
- Glider Classic by Soft Dorothy
- Groove Coaster by TAITO Corporation
- Hero Academy by Robot Entertainment
- iBlast Moki by Godzilab
- Jetpack Joyride by Halfbrick Studios
- Lemurs Chemistry: Water by New Lemurs
- Leo's Fortune by 1337 & Senri
- Lode Runner Classic by Studio Voltz
- Lost Cities by TheCodingMonkeys
- Machinarium by Amanita Design
- Minecraft by Mojang
- Monsters Ate My Condo by [adult swim]
- Monument Valley by ustwo
- Osmos by Hemisphere Games
- Paper Toss by Backflip Studios
- Robot Unicorn Attack by [adult swim]
- Scribblenauts Remix by Warner Bros.
- Shufflepuck Cantina by Agharta Studio
- Smart Sokoban by Patrick Stein
- Sneezies by Chillingo
- Space Invaders Infinity Gene by TAITO
- SpellGrid by Song San Hong
- SpellTower by Zach Gage
- Spirits by Spaces of Play
- SPY mouse by Electronic Arts
- Strimko by Grabarchuk Puzzles
- Super Monkey Ball by SEGA
- Superbrothers: Sword & Sworcery EP by Capybara Games
- Tengami by Nyamyam
- The Incident by Big Bucket Software
- The Room by Fireproof Games
- The Room Two by Fireproof Games
- The Secret of Monkey Island: Special Edition by LucasArts
- Ticket to Ride by Days Of Wonder
- Tiny Wings by Andreas Illiger
- Trainyard by Matt Rix
- Triple Town by Spry Fox
- Waking Mars by Tiger Style
- Whale Trail by ustwo
- Where's My Water by Disney
- Words Play by Stand Alone
- World of Goo by 2D BOY
- QatQi by ZWorkbench, Inc
In addition, some games not available for iOS:
- Botanicula by Amanita Design (Mac)
- Braid by Hothead Games (Mac)
- Civilization V by Aspyr Media (Mac)
- Crystal Quest by Patrick Buckland (Mac)
- Fallen London by Failbetter Games (Web)
- Fez by Polytron (Xbox)
- Gone Home by The Fullbright Company (Mac)
- Journey by Thatgamecompany (PS)
- Kerbal Space Program by Squad (Steam)
- Portal by Valve (Xbox)
- Rocksmith 2014 by Ubisoft (Mac)
- Skate 1, 2, and 3 by EA Black Box (PS/Xbox)
- Star Control 2 (Mac)
- The Legend of Zelda: A Link To The Past by Nintendo (SNES)
- The Neverhood by DreamWorks Interactive (PC/PS)
- VIM Adventures by Doron Linder (Web)
Thank you to everyone who gave a recommendation!