Since we’re talking about free to play games, we should mention Petite Rock Shooter: Pursue the Mystery of the Sexy Planet is on iOS now. Imageepoch, makers of Black Rock Shooter for PSP and Last Ranker, developed this bullet flicking RPG.
You play as Petite Rock Shooter and have to shoot your way through levels. Destroy all of the enemies and a sexy boss waiting at the end of the stage to win. Petite Rock Shooter has different items you can customizer her with. Some of these cost money and it looks like the game uses a "gacha" system where you get random items as if you were getting a toy from a capsule machine.
Have an iPhone (3GS or higher) or iPad. Login with a Japan region iTunes account and download Petite Rock Shooter: Pursue the Mystery of the Sexy Planet right here.