First up we have Temple Run 2, from a series which has often been duplicated but rarely replicated. The sequel's biggest boon is the revamped engine, which is far prettier this time around. There's also a lot more verticality, as levels heave and sway with hills, traps and ropes. As an added bonus, it's free-to-play and is surprisingly not very demanding of IAP. It's there, of course, but you'll get a large amount of enjoyment without having paid a cent.
Next is a strange one called Final Fantasy: All the Bravest. Imagine the graphical style of the original 8-bit Final Fantasy games, but with the gameplay of, well, I'm not really sure this is gameplay. You tap on the screen a bunch and the guys attack until the monster is dead. There's no real strategy to it. As evidenced in the video...