All of these are for Android. They are not my full collection, but those are the ones I found most addicting.
OctagonMinimalistic runner with 3 contols but a ever-increasing difficulty. You can choose level-based, in which certain levels will add new patterns and each level has a set speed; or endless which has increasing speed and basically a race for time ala classic runners. I would not say it's your standard runner game however, not by a long shot.
Fast FingerWhile having a commercial pay-to-play business model, the game is in essence free. The restriction is that you have 40 lives max, each minute you gain a new one wether the game is on or not, and each time you finish a level with Gold you get a new one as long as you didn't finish it before,. Outside of that, you use your finger to not hit walls, spikes or whatever the game throws your ways to get to the finish line. Similar to those maze games where you are supposed to not hit the walls with your cursor on the PC.
Math EffectSolve math problems as fast as you can, endlessly or 10 as fast as you can. Mistakes can be made in limited numbers, the fast problem solving is the main mode. This game may not be for everyone but feature-wise it's more than what meets the eye, even having some sort of levelling system.
CircixEach square needs to have as many connections as listed, and you can only create non-overlapping connections between squares horizontally and vertically. You win when all squares have the amount of connections as the number on them.
MinesweeperNothing to explain here. This is the best Minesweeper app I found on the Android, offering neat design, responsivity, stats tracking and all dat good stuff.
Please note all of those games are playable without internet connection.