Flappy bird is worth playing
If you want to break your phone in a fit of rage
My Boy is a great for a free game boy emulator. Don't forget, you need
ROMs.
FPse for Android is a PSone emulator. Not free, but for a couple bucks it's totally worth it. One of 2 apps I've ever paid for. Very good compatibility and again, need to download ROMs of games you want to play.
Also need to download the bios, google "SPCH1001.BIN". Note that there are different versions with slightly different numbers for different regions, eg Europe/Australia or Japan. 1001 is US, but any should do. You might have better luck finding a download of the bios on torrents since it's not exactly legal to share. eg disclaimer, you should download only if you own a PSone.
If your phone has OTG support you can plug in a simple USB game pad via an OTG cable (like a dollar off ebay). I've easily used a Chinese analog PS controller ripoff after assigning button controls. Much better than on screen controls. I've considered bending up a wire frame which would hold phone above controller for better convenience, if I get the chance to play.
Clever Contraptions is basically a clone of The Incredible Machine, if anyone remembers that classic Windows puzzle game. The lite version is very limited if I recall correctly, but it's worth trying out.