I don't play a lot of games, but the types that I usually do end up spending time on are puzzle games and word games. Perhaps the one game I've loved the most over the past few years is Monument Valley, a mind-bending 3D puzzle game in which you help a princess -- Ida -- find her way through complex optical illusions. The developers, ustwo, have set the price of Monument Valley to "free", and if you haven't yet enjoyed the game, download it today.
Monument Valley was both a winner of an Apple Design Award and the Apple Game of the Year in 2014. There are some expansion packs available (Forgotten Shores for $1.99 and Ida's Dream), and it's sure to keep you busy for days. It's been updated recently to run on the iPad Pro, so if you own one of the big tablets, you must get Monument Valley while it's free.