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There are many casual good titles without microtransaction. Especially if you like the casual puzzle (like match-3), hidden object, and time management genres.

• Lifeline
• KOTOR
• Chrono Trigger
• Minecraft

Those games gave me a good amount of playtime without microtransactions

I recommend Iron force, have enjoyed the game for quite a few hours. :)

The Bard's Tale :> (you have to buy it for like 1.5$ but it's not pay-to-win)

Fallout Shelter!

Unfortunately, I don't have many suggestions mainly because I'm searching for a nice non pay to win game. So I'll eagerly check out some of the replies here.

Here for suggestions too :)

Loot & Legends, though I haven't played it personally, not using smartphones at all.
It's a derivative of Card Hunter, and the players from there that've tried it have good things to say about it.
There is the option to pay for boosts, and that's grossly overpriced, but they're not actually too meaningful to the game; and you can apparently play-to-earn the same boosts anyway.

It's fully PvE (unlike Card Hunter, which has a PvP side), and both are based around collecting loot, and neither have any pay-to-win elements, though they do have expansion content to unlock in the campaign.

In any case, they're both well made and free, so you can at least give 'em a try ;)

Shattered Pixel Dungeon is one of the greatest games you can find on android.

Plants vs. Zombies 2

I was addicted a year ago, but generally almost all Android games are casual games and not comparable to PC or console games.

I used to play Game Dev Story. I think I bought it for a dollar or so. It's a nice micro-managament simulator and quite fun, full of references to gaming history. It's from japanese devs Kairosoft, they have a lot of that type of games.

The only game I do play, occasionally, on my phone is EA - UFC.

Well i'll recommend you my friends game, circle mania. I think it's really fun and its definitely not pay to win because there's no in app purchases. Only adverts.

I'm guessing you're looking for free games?
Pac-Man 256 is new and fun and Crossy Road is made by the same devs, its also pretty good and has one of the best monetezation set ups in all of f2p gaming (I havene't played in a while tho so hopefully that hasn't changed)
Alphabear is also fun but they sort of have a pay or watch ads to play mechanic set up, where you can only play so many games at a time unless you want to watch ads or pay money, which kind of sucks.
As someone else said, fallout shelter is a lot of fun
and I spent a lot of time playing Galaxy Hero before i was able to get more games, its a really good space shooter with RPG elements.

You could try and search for games on Amazon Underground, even the in app purchases are free. I would recommend Puzzle Retreat, The Where's my (Water, Perry, Mickey. Water 2 was kind of annoying with the lifes but since in app purchases are free this way it might not be that bad), Cut the Rope.

I'll try to list some that haven't been mentioned yet. I don't know how to do text hyperlinks, sorry.

Jetpack Joyride and Deep Loot are superb examples of f2p games done right. Both have microtransactions, but they aren't necessary. I bought the coin doubler in each game, though.
https://play.google.com/store/apps/details?id=com.halfbrick.jetpackjoyride
https://play.google.com/store/apps/details?id=air.com.monsterandmonster.DeepLoot

Little Alchemy is like doodle god but bigger and with a lot less annoying bells and whistles. Also, completely free with no ads.
https://play.google.com/store/apps/details?id=com.sometimeswefly.littlealchemy

If you like riddles, A Year of Riddles and the sequels are good.
https://play.google.com/store/apps/details?id=net.pyrosphere.riddle

If you like crossword puzzles, a good client is Shortyz.
https://play.google.com/store/apps/details?id=com.totsp.crossword.shortyz

The PathPix series is a lot of good, semi-mindless fun.
https://play.google.com/store/apps/details?id=com.kpixgames.PathPixLite

So is Glozzle.
https://play.google.com/store/apps/details?id=com.magmamobile.game.Glozzle

If you liked Glozzle and want something similar but better-looking and more involved, try Blueprint 3D.
https://play.google.com/store/apps/details?id=com.FDGEntertainment.Blueprint3DHD.gp

Monument Valley is sort of expensive and a little short but 100% awesome.
https://play.google.com/store/apps/details?id=com.ustwo.monumentvalley

Finally, Smash Hit is probably one of the best mobile games ever made.
https://play.google.com/store/apps/details?id=com.mediocre.smashhit

My experience has been like yours--a lot of stuff sucks, and I hate pay-to-play. Here are a few things I enjoyed:
-Trainyard - it's a puzzle game like SpaceChem. It's quite good. (SpaceChem itself is available for android, but I prefer it on PC. Still, it's my all-time favorite puzzle game.)
-Boardgames like Carcassonne and Smallworld (if you enjoy the real-life versions, the digital versions aren't bad).
-Simple puzzle games like LYNE, Buttons and Scissors, etc..

Populus Romanus is a fun little hex-based strategy game. There is a demo of it, and it's representative of what the game has to offer.
Wargame of 1939 is by the same company, and once again you have a free demo. I found this one to be more challenging (if that's a good or a bad thing depends on what you're looking for, but I enjoyed the challenge)
Call of Cthulhu: Wasted Land Turnbased tactics game set in WW1, with mythos-creatures. I enjoyed it, but it drains your battery quite fast.
Anomaly: Warzone Earth It's not identical to the PC version, but it's obviously similar.
World of Goo Seems to be mostly identical to the PC version. Fun puzzle game, well worth your time & money.

No one has mentioned "Only One" by Ernest Szoka?

Also, "Punch Quest", which is a lot of fun and has a quirky sense of humor.

Both free, both fun, both non P2W.

I tend to buy mostly PC games on Android.

Kritika

King of Dragon Pass.

this is quite fun: RGB Express

Clash of Clans