Currently two:

War Thunder - It has so many issues from the grind, to unadressed design issues (IE 10kg HE shells doing no damage on a direct hit), to balance issues including p2w vehicles. That said, under all the shit, theres a solid foundation, and no other game comes close to replicating it.

Super Auto Pets - Its an autobattler streamlined to the point where its the perfect casual game when I don’t feel like anything else. It also doesn’t have any of the normal f2p traps, and is monitized purely on cosmetics that can also be earned for free.

Edit: I guess Dota 2 counts too. I put a ton of time into that. I’m not a particularly good player, but its one of the best team-based games out there, so I enjoy playing it with friends.

Warframe

Warframe ever since 2012!

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. !pixeldungeon@lemmy.world
• 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 !cataclysmdda@lemmy.ml; the subreddit is much more active.

PC - Path of Exile - This is an ARPG similar to Diablo 2. It has very well defined terms (outside of a few edge cases) that help guide your build creation. Lots of community support. They release a new league with content and updates every 3-4 months. While F2P, stash tabs are a useful purchase if you enjoy it long-term. I’ve been playing since 1.0 (over 10 years ago now)

Android - Idle Obelisk Miner - There is some initial manual mining, but then you’ll unlock drones and bombs for mining. It’s better as a screen-on idler, but can be played screen off, but much slower. In terms of an idler, I feel the pacing is done very well. (30 days of play time in game as of now)

I recently picked up Crossout again when browsing free games on xbox. The Battle Bots x Lego kinda thing works for me, sadly it’s very pay to win so you hit a certain level and then the fun is gone.

I have put some 1400 hours into Rocket League, even though I’ve been playing it since it wasn’t free. Easy to learn, impossible to master. Sadly the community is super super toxic, so it’s more fun if you have a friend or two to play with.

Warframe and Lotro are terminal illnesses for me. I’m never done playing them. It’s an endless cycle of dressing up a hobbit in Middle Earth or dressing up a Warframe in space.

Does wordle count?

Thinking about getting back into Crossfire. That was a super fun time during high school with a good friend about 15 years ago. Maybe it’s just the nostalgia but I remember some quite fun modes like Ghosts.

Xonotic, tf2

I don’t remember when Alto’s Odyssey became free to play on Android, but it’s honestly such an amazing game. Its prequel is pretty nice too, but I like this one better.

I used to be addicted to Super Starfish too. I’m even pretty close to completing it, but just never had my chance to do so because… reasons. I would love to see this game on the Nintendo DS.

I played the original Sonic trilogy. It was fine, I guess.

The Dadish series was super annoying and very infuriating despite looking like something a child could complete in one sitting.

Bean Dreams was absolutely phenomenal, though. I loved every second of it. Why on earth did they have to take it down from app stores???

I played Okay. It was okay.

Bart Bonte’s “color” series of games are also pretty fun to play through. You actually can finish all of them in one sitting if you’re brainy enough to do so. I did. “Black” was my favorite, since you get a glimpse of the Belgian flag at the end (Bart is Belgian after all).

I even played Goat Simulator on mobile (not the sequel, the original). For some reason I enjoyed that one the most despite how very obviously limited the mobile version is.

Conclusion: I like very niche categories of mobile games.

Warframe and Warthunder. Lot of war happening, now that I think about it.

I’m starting to get a bit burnt out on Warthunder, though.

Predecessor is the best MOBA I’ve ever played, and it’s not even out of early access yet. Right now just grinding Brawl because it’s braindead action but the normal gamemode is also good.

Super Auto Pets and Bloons TD Battles 2

I have not come back to it in awhile, but Mobile Legends bang bang. It’s a tower rush game (league of legends knock off) that is free to play, with plenty to buy for those that want. Besides some of the cosmetic stuff (skins and stuff) anything can be gotten through grinding.

It’s 5 on 5 tower rush, with lots of different characters. I had gotten quite familiar with playing a few, and for awhile really knew a bit about playing against most of the regularly seen characters.

Nowadays I get the urge every few months, update app, play for a week or two then put it down.

Sim city build it also stays on my phone, as it is a peaceful and colorful game. Easy to play for 10 minutes or go in and out of on a long ride.