That's a really wide question. I'll give you my list of answers.

Here are my top three:

• Shattered Pixel Dungeon, a roguelike descended from Pixel Dungeon. It's strayed quite far afield from the original PD, but I think most of the changes are good.

• Mindustry, a hybrid tower defense and systems-building game. I've heard it compared to a game called Factorio, but I've never played that, so you'll have to take it with a grain of salt. Sorry.

• Forkyz, a crossword app, which is a fork (appropriately) of a game called Shortyz. It allows you to download daily crosswords from bunches of sources for free and play them at your leisure.

• Chip Defense, a tower defense game themed around computers. It's really fun if you like computers and/or tower defense.

• Space Trader, a text-based game heavily inspired by Elite. Travel a galaxy, trade goods, blow people up, complete quests, buy a moon.

Here are some games on F-Droid that I'm not going to link, because i don't know how they do on Android, but I love them on PC:

• Luanti, which used to be called Minetest. It's an open-source voxel building game engine (like Minecraft). It's very scriptable, and you can build a lot of stuff with a little knowledge and looking at examples.

• Battle for Wesnoth, a turn-based hex-grid strategy game with day/night mechanics and multiple campaigns, both included and downloadable. And it's got multiplayer too!

• Endless Sky, a spaceflight game which borrows heavily from the Escape Velocity series. If you like the concept of Elite, you should check it out.

• OpenTTD, an open-source version of the classic Transport Tycoon Deluxe, but so much more.