These two platforms don’t get enough credit frankly. Mobiles especially! There’s some really good games out there and a bit of googling revealed this - http://www.theguardian.com/technology/appsblog/2013/aug/14/best-android-games-2013 - which led to some outstanding games. Btw, Guardian’s entire technology/online section is surprisingly good, especially regarding games. I’m on android but i’ll be surprised if there are many games that are iOS/android exclusive. I have no clue about windows phone so sorry nokia users!
It would be helpful if people could list the freemium options present in these games or not. These make or break mobile games for some people, especially those with ad banners. Prices will vary between regions btw so keep that in mind. I’m in India and prices can be good here. Kingdom Rush is 60 rupees (60 pence!) and its sequel is 200 (1.99 pounds) for a comparison basis. Yes, my work keyboard lacks the pound sign. 
Currently playing:
Frozen Front, intrusive freemium - old school, hex based, world war 2 turn based strategy. Yes, you heard right and somewhat reminiscent of Panzer General. Its well balanced, has tight mechanics and I like how the AI’s turn is presented as an old school sepia toned movie with full whirring sound. Multiplayer is available which is a really nice bonus as human vs human is where this game really shines. Not the hardest TBS i’ve played but good in short bursts. Does have an annoying ad banner however, in fact so annoying I paid. That aside, the standard freemium purchases are available but as its not the toughest game so I doubt most of us will pay for anything (aside from that ad banner, holy shit).
Cubed Rally Redline, totally free!! - utterly charming and brilliant endless runner. Lovely 8 bit inspired look, controls perfectly, runs like butter down the side of a non-stick hot pan, absolutely no freemium bull anywhere and adds a lot of interesting mechanics to what is now a well traversed genre. Apparently, this is all 1 guy too. Did I mention the awesome music from 8bitweapon?
Punch Quest!, 69p but incredibly generous rewards and optional freemium - you know how some games just put a gigantic grin on your face and you’re screaming in your head “Holy shit, I love this game”? Punch Quest is one of those. Part endless runner, part sideways scrolling brawler with a control scheme that suits mobiles perfectly. Pick avatar - berzerker/valkyria - start game, wreak havoc. Don’t let the simple look and controls fool you from what is a surprisingly well realised brawling mechanic that even manages to incorporate blocking just right.
Flow Free and Flow Free Bridges, free with optional freemium - standard connect the dots puzzler with hundreds and hundreds of levels on different sized boards. Simple, effective, well presented, a gargantuan generosity with the number of levels and an excellent mechanic in the Bridges sequel to keep things fresh and freemium kept well out of sight. Same developers as Punch Quest above.
Robot Unicorn Attack 2, optional freemium - yes, same robot unicorn as the one on the adult swim website. Lovingly updated for phone and surprisingly good looking game too. Its utter ludicrousness is ever present and in a spot of genius, they basically forced my hand to buy a song from their store - namely The Touch, I…I couldn’t resist! The combination of winged flying unicorn with rainbow streak and this song was too much. A large number of customisation options for your unicorn too. There’s also some online shenanigans in two sides battling each other but haven’t dabbled yet so no clue.
Kingdom Rush and Kingdom Rush: Frontiers, 69p and 1.99 pounds and both with optional freemium - outstanding tower defense games. Very old school, ruthless with balance and challenge, has heroes + towers and on hard and above will joyously crush your spirit.
On browser, Cookie Clicker - I seriously cannot stop playing this.
