This app was mentioned in 6 comments, with an average of 4.50 upvotes
A recent favorite is a $2 indie puzzle game on mobile called <em>Odd Bot Out</em>.
With plain levels, crude audio, no characters, no dialogue, and no text, the game uses only basic symbols and just a skeleton of a story: your name is Odd, you're a Bot, you fail a standard test, get thrown into the recycling bin, and must solve 100 puzzles to get Out. It's all in the title.
OBO takes the "figure it out" approach to game design, which I love and respect immensely. No tutorials. No hand-holding. No bullshit. Just experiment to learn what the blocks do. And with scaffolding, its later concepts build on its early concepts, so the puzzles maintain variety.
All in all, an earnest and intelligent game easily worth the price of a soda.
Odd Bot Out on iOS and Android.
It's $2, it has 100 levels, the art style is simple, and the gameplay is straightforward. OBO is one of my favorite puzzle games ever.
I have my own list of recommended games, [also posted on reddit](/r/AndroidGaming/comments/4aa7q4/i_know_there_are_actually_good_android_games_out/d0zbevq).
In this post, I'm building a different list, even though the intersection is large. You know that aiming for "long play sessions" is pretty subjective. Since I like puzzle games, I can play one repeatedly for quite some time, even on PC. So, naturally, my list has several of those.
Originals (they usually have short levels, anyway):
Ports:
Emulators:
P.S.: As a public service, I believe you should link all the suggested games. Sometimes searching them on the play store is a pain. Even worse if people are reading this reddit post on mobile.
I believe it to be the weakest of Martin's games. After phenomenal Odd Bot Out (https://play.google.com/store/apps/details?id=com.martinmagni.oddbotoutpaid) which I loved the most (even though level editor was never released for this one), Mekorama was a disappointment (even though it had a level editor). There is Fancade nowm though (https://play.google.com/store/apps/details?id=com.martinmagni.fancade) - an almost endless supply of arcade games for mobile which is heavily supported by community (with new cool games released almost every day). I highly recommend everyone to try it out.