I was originally going to write a blog entry on iOS retro ports. The problem is that retro ports on iOS are universally pretty terrible. Games made to be played with a joystick, D-pad, or keyboard simply don't convert well to the touch screen.
Some games, however, do work very well on iOS. Puzzle games in particular flourish on iOS, for the same reason they do on the DS; the touch screen is well-suited for the genre, allowing you to manipulate puzzle pieces or the puzzle board in a direct, intuitive manner. The impreciseness that sometimes comes with controlling a touchscreen with your finger can be frustrating in more action-oriented titles, but many puzzle games are much more forgiving of this device flaw.
Unfortunately, on the app store the success of one puzzle game will inevitably be followed by 50 sub-par clones. The iOS store is so overrun with puzzle games that it can be difficult to find one worth playing. Need help sorting through the masses? Here are a few of my favorites: