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I play Best Fiends, a decent f2p, the thing is after certain level, it gets hard so you have to try a lot of times in order to finish the level.

Pala Dog

Only have 3 games on my phone:
The Bards's Tale, Goat Simulator and Fallout Shelter.
I used to play PlayStation games on my old phone, some jrpgs like Final Fantasy, or Crash Bandicoot :D

Age of Strategy! It's free, non-profit, no adverts, no in-game purchases, the dev only gets money through donations (he does it in his free time)!
It's also awesome! So check it out!

Hearthstone!

Hellraid is a pretty neat 1st person puzzler with gorgeous visuals.

StarCommand is a pretty nice mix of managing your ship and exploring the universe and fighting a lot of dogfights which means controlling your crew to defeat the opp ship.

Get youself TETRIS, I didn't need other games for 3 years now.

Some shameless self promotion Birth of the Empires. Mind the high learning curve as there is no tutorial yet.

NES and SNES emulators with ROMs (starting with Contra and ending with Final Fantasy first games)

F2P I enjoyed on mobile:

• King of Thieves. Yes, some of you may think this is P2W, but I am in Onyx League(the 2nd last league) without spending a thing.
• Piano Tiles 1&2, although the 2nd has energy system a stuff, it's pretty fast to recover, and you can have 30 lifes at once. You spend 1 life to play one music, so I think it's fine.
• Tiny Troopers. It's fun :P
• Sky Force, it's a mobile classic. I've played in my older Symbian phones, and it's hell fun...If you like hell shooters.
• Card Crawl. This is more like a demo, but it's still has some content. And it's fun. It's extremely casual tho.
• Alien Shooter. I haven't played the pc version(or the mobile, I'm currently downloading :P) but it seems it's a remake of the game. You may give it a try.
• Green Ninja: Year of the Frog, or anything Nitrome. Besides some annoying ads, it's fully free.
• Follow the light. It's a fun plataformer. Timing is the key. Don't walk on shadows. I beated the game, so it's not impossible ;)
• QuizUp. As the name says,it's a Pvp Quiz game.
• The King of Fighters. It's a HUGE game, but it's fun. The only probrem is that you can't play agaisn't someone online.
• Dead Trigger. Zombie FPS game.
• Cicle the dot. Once you easy, but at first it's a bit challeging.
• Ultraflow. It's hard, it's challeging, but I couldn't stop playing.
• Aces Spades. It's a classic cards game. How P2W can it be?
• Emulators! Just make sure you already have the games.

Have fun with this list :P

Pew Pew 2 is great! Also, Telltale games, I'm currently playing Tales of the Borderlands on my phone.

Alphabear. There are IAP but its not P2W.

Chronicles of Inotia 3, same deal.

Letter Quest: Grimm's Journey

DraStic: https://play.google.com/store/apps/details?id=com.dsemu.drastic&hl=en
And you can play any Nintendo DS game on your phone. Ace Attorney series, for example.

Get a SNES emulator.

trials frontier