Time for me to recommend free games!
99 Rockets: rockets running on predetermined rails, and shoots straight ahead on tapping. Good luck with your timing the shots and deciding which one to shoot. 99 levels, so go for it!
Combo Quest: reflex game where you time your tap to attack, and adds an element of strategy whether to use your combo bar (built by combo, duh) as a super move.
Soda Dungeon: an RPG where you recruit heroes to clear a 100-floor dungeon, comprised of 5 20-floor levels. The beauty of the sprite and the music is great, and a good time waster. Auto mode, too, to get through some slog. Items abound, so enjoy~
Dice Mage: if you don't like the above, this one is a more streamlined luck-based RPG decided by, yep, dice rolls. Loot also bases on dice roll. Add in the ability to re-roll with a price and you got a decent RPG that you can aim to clear as quickly as possible. Do you feel lucky, punk?
Now, for paid games:
Downwell: THE roguelikes for mobile. Tight mechanics, great control, simplistic and clear presentation and fitting audio for atmosphere, this is one action roguelikes you can't miss.
Hoplite: a hex-based strategy game where you clear randomly generated floors to reach deeper in the dungeon, with only 1 power up-per-floor to help you. What you pick can save you or kill you, and certain skills need you to give up your health bar to get. Think a tile at a time, go a mile on a dime.
Time Surfer: endless runner where you try to time your diving from mid-air into slopes to get a speed boost. Sounds hard? There's a reason why you can rewind time. With a funky soundtrack, bounce and surf your way through obstacles and grind against planets. Sold?