Seems we've done this before, but, Okay!
I mostly play emulators, but I'll list some I keep going back to:Death Worm
Worm-type game but you can jump out of the ground to snag camels and helecopters out of the air for points.Gish Reloaded
Gish for PC went open-source and it was ported to Android. It's a great physics-platformer and this port can use the accelerometer if you choose.Grabatron
Abduction game that uses the accelerometer well. Tap the screen to grab people, and things to complete missions. Throw or drop heavy things to destroy buildings or kill.Momonga
Pinball game with incredible graphics and well-built levels. A few light mini-games between stages and cutscenes.Plasma Tennis
Vs. Computer Pong, but with fluidic physics added and shown.Sonic (1
Option for spin-dash=fixed gameplay.Super HexagonTemple Run 2Gear Jack
This platformer auto scrolls - you control when to slide or jump. That means I can play it on a small screen without a controller. Click bonuses for attacks and points. Well designed levels.Ridiculous Fishing
Guns and bombs and chainsaws to get the big ones at the bottom. Very addicting.Cut the Rope HD
Kinda reminds me of The Incredible Machine. Really well designed puzzles.Fun Putt (original
Ya, I like mini-golf games. I play Fuzzy's Golf in Dosbox more, but these are great.Hexagon Unlim
The Puzzles are so complex, but fun!Hexxagon
I love Hexxagon (originally for dos) and this is the best upgraded one I could find. Levels with multiple enemy colors are really well designed, and there's so many levels!JezzBall Classic
Just like the old Windows 3.1 version!Monument Valley
Uses optical illusions for uncanny/impossible terrain you have to modify to navigate through.Tangram
So many Levels!Tetris
Touchscreen controlled Tetris.Uncle Worm
The worm game (Pizza Worm, etc) with many control options.Puzzle Prism
Kinda like 3D tetris?Mr.AahH!!Glow Snake
Another worm game...Canabalt HDCatbug!
Love Catbug, so this is the "chopper" game I keep on my phone.Ground Effect ProMX Mayhem
One of those motorcycle throttle physics games. I tried a few and like this one best. Customizable controls and accelerometer optional.Riptide GP2
Like WaveraceSpeedx 3D
(Baldur's Gate)Ur-Quan Masters
(Star Control II)Wargus
(Warcraft II)Dune 2OpenXcom
Dunno which are exclusive, and many are just rehash/ripoffs of previously released games, but I play all of these occasionally.
edit: Added details...