This comes around every few years, but I haven't seen it recently: What are the best portrait games available for iPhone? Extra points for those optimised for one-handed or brief play.
Oh, I should have given (some of) mine! Easy Harmony Card Crawl Hoplite Power Grounds Monument Valley Sorcery series
Great little war game 2 Magic the gathering quest or whatever that new release is Pretty much most roguelikes: Cardinal quest inethack Downwell Spellcraft Card kombat Galaxy trucker Card dungeon
Many of the above I haven't tried so glad to hear of those suggestions. Personally, I definitely recommend Monument Valley - the first version just went free as well so perfect time to download it. It is an incredible game in my opinion and worth spending on the update. Another game I recommend and which I keep re-adding on my phone is Crossy Road. Quick gameplay, really cool how they switch things up with the characters (they include characters from other games - clearly for cross-promotion but I like how subtle that is). Last but not least - Polyblast (Disclaimer: I am part of the team who created it). Its a cool (portrait) space-invader like game that has smart gameplay. I recommend you check it as well (and if you can give me feedback even better )