All the native Android games I have played have already been suggested, so I could suggest using GameNative or similar to emulate some neat indie titles.

If you like retro games, you could also emulate your legally obtained ;) titles from GameBoy to PS2 to Dreamcast. I like using Retroarch for most of my emulation on my computer and I believe it exists on Android too. Dolphin is great for GameCube and Wii games, NetherSX2 for PS2. There are plenty of other good emulators too, each with varying degrees of feature set, compatibility, and stability.

On iOS, you have Delta (which focuses on older Nintendo titles), and not much else (Apple’s fault for having closed app ecosystem and not having the best support for things like JIT)