If you mean free-to-play in the sense of a commercial game that one can play without payment, but where it is supported by data-mining or in-app-purchases or ads, I can only off-the-cuff recall playing a few games in that category:

• World of Warships. I played one round against humans.

• Defense of the Ancients 2. I played one round against human players and some time against the computer.

• Fallout Shelter. I didn’t like it much, though I do like the mainline Fallout series.

• I remember some gamebook game on Android that showed ads at the bottom.

I’m not playing any of those currently. Broadly-speaking, I don’t like the model. I’d rather just pay up front.

If you’re talking about free-to-play-with-the-aim-of-selling-you-on-a-larger-game, I’ve played plenty of those – in the 1990s, shareware and demos were a common way to promote a game. But they’ve kind of fallen out of favor in terms of DLC. I don’t think I’ve played any of those for a while.

If you’re talking about entirely free games, then I’ve played plenty of those. I think the two that I’m currently playing off-and-on, both open-source, would be:

• Shattered Pixel Dungeon, an Android roguelike. [email protected]
• Cataclysm: Dark Days Ahead, a (mostly PC; there’s an Android build and you can play it on a touchscreen, but it’s really better-suited to a keyboard) open-world roguelike. There’s a not-very-active Threadiverse community at [email protected]; the subreddit is much more active.