Recs.
Updated
Pixel Dungeon is a traditional roguelike game that is free to play with only one in app purchase for optional donations.
SpecsUpdate
Pros
Pro Great variation in items
Next to the typical selection of buffs, de-buffs, potions (that can be either consumed or thrown), weapons and armor (that have to identified and can carry with them bonuses and curses), there are also less common items like random teleportation scrolls, map reveals, etc.
Pro Maps and items are randomized allowing for lots of replayability
In a true roguelike fashion, levels are randomly generated each time a new game is started. And Pixel Dungeon goes one step further by randomizing effects of all items as well so it's impossible to tell if a dropped item will have a positive or a negative effect based on its sprite.
Cons
Con Too random
A lot of people associate "roguelikes" and "random." That disregards a lot of the work that roguelike developers put into making sure that a good roguelike is pretty consistent and well balanced. After winning Pixel Dungeon it can feel like it was because the random number generator smiled upon you. After losing, it can feel like it was because the random number generator just wasn't feeling it this time.
Compare this to something like ADOM (no, it's not an android game) where when you die because you got attacked in the moving forest it's because you made the dumb decision to use a fire spell.
Con Overly random
A lot of people see roguelike design as being based around randomness. It's actually a far more precise set of balances than that. A lot of roguelike developers shy way from "randomly generated content" in favor of the term "procedurally generated content." The reason for this is that a well designed roguelike is well balanced enough that if you lose or win, it's all because of the actions you took.
Pixel Dungeon has a habit of sometimes generating dungeons that are basically impossible and sometimes generating dungeons that are laughably easy.