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Hill Climb Racing (alltime fav :D)

Pixel Dungeons

World Of Goo. You probably won't find it on Google Play, yet if you want, I will find it for ya. Trust me, you will like World Of Goo

TÚ!

wwaazzzzaaaaaaaaaaaaaaaaaaaa

Doodle Jump? :P

Gravity Defied

The Silent Age {Only episode1 is free - But is long x}

Temple Run, Temple Run 2, Minion Rush, Jetpack Joyride...

Colossatron, Fruit Ninja, Flappy Bird

Try installing the Amazon App Store. You'll need to authorise Android to download from unauthorised sources, but they give away a paid app for free every day. They're not always good, but worth a look :)

One of the first android games i really liked that was addicting and fun was slam bots Which is free, another but cost money is Game Dev Story , so much fun.

http://www.amazon.com/mobile-apps/b?node=2350149011

every day something new

Box Breaker https://play.google.com/store/apps/details?id=com.demilp.BoxBreaker

Age of Civilization, Zombie Dash, Beats. These are the only games that I keep on my phone and quite enjoy them. :p

Duet, Ingress, Dumb ways to die, Fruit Ninja, Heroes of Loot

Dead Trigger 2 :D

A N64 emulator.

Yhea, kind it dont count but i am having fun playing ocarine of time again in my free times.

Why has noone proposed Godus so far? It's not that bad on Android.
You could also check Make them fall, or stuff. Also, Amazon are giving, or have been giving away, 5$ you can spend on apps in their store. You can get some nice little games there, and some paid games are sometimes given free.

curently playing real racing 3 and sniper 3D .played clash of clans some time ago great game , but u need a lot of patience with it

Dragon Coins is a pretty addictive free game that caught me. It starts out very hand-holdy and seems boring, but if you can endure past the invasive tutorial steps it gets pretty good. It's a monster collection/evolution battler, where the fights are worked out with one of those "coin pusher" arcade games. Where the coins fall determines which of your monsters attack (with various monsters requiring between 1-3 coins before they trigger a strike), with the enemy monsters attacking on a delay based on how many coins you have dropped (with faster enemy monsters hitting you every 6-ish drops, and slower ones every 15).

It does try to catch you with "Hey you can totally pay money and get access to these higher-end rarer creatures faster!" but you can easily play it without spending a penny. To get access to those rarer high-end creatures you have to do something akin to an 'achievement' on each area, which then gives you a few of the premium coins that you can save up. During the week, you can engage in desynchronised PVP for 'battle coins' to spend on random monsters from a separate hatching list, and during the weekends you can attack a special boss encounter for 'hero coins' for a different pool of monsters (which chain-evolve up to a rare monster). If you place in the top 500 scorers you get a free ticket to spawn one of the premium-currency monsters, and above 300 (or was it 200?) you get a ticket for the ultra-rare expensive spawns. It's not hard to do, it's just that you need to check in more frequently to make sure you keep expanding your score when you can.

It does work on a stamina meter kind of deal, but you get plenty of stuff to do each day, and you get rewards for logging in each day, which includes occasional premium items. It's just nice to find a free game that doesn't utterly hard-lock stuff and that isn't too grind-heavy.

You may end up hating me for suggesting this, if you can get past those damn tutorial things xP

Shadow Fight 2

I would also recommend keeping an eye out for the humble android/mobile bundles, because they're a great way to pick up some of the more involved titles at a cool discount. I mostly get those because of games I've never heard of~

Thief Lupin (and the sequel Thief Lupin 2) are great little Android games. You control a little thief and your task is to collect all gems and avoid various traps as you ascend the game levels.
Google Play

Then there is also Time Traveling Thief, that's a little logic puzzle. You are an ancient... keeper of sorts who is time traveling to collect mystical shards. In each levels, you have a set amount of turns that you can use to obtain a shard and get to the exit. There are bad guys patrolling the locations, so you have to plan your moves cleverly to avoid or eliminate them.
Google Play

Last but not least, my third favourite Android game is called Obslashin'. You control a little guy who hacks&slashs his way through the lovely drawn locations, collects coins and power ups and tries to stay alive as long as he can.
Google Play

I played all three of them for a long time (I have Sony Xperia M, by the way), all are very fun and addctive. I recommend you check them out, at least one of them may hook you up for quite some time! :)

Castle clash, Icy tower 2 :D