The Sky is Falling
Filed directly under the "yes I'm old enough to remember the games this game was inspired by" category, The Sky is Falling from Ovine by Design is a retro arcade game that would have to revert to lines scratched in the sand to be any more old school. It's built around a simple mechanic that gradually gets more difficult as you play, offering up a crazy premise and a lot of gameplay mastery that only comes with practice, practice, and probably some more practice!
The basic idea is this: the sky is falling, a boulder is rolling, the stalagtites are crumbling, and you are running. Armed with nothing more than an excellent pair of calves and an infinite supply of spanners, your character steadily plods from left to right, wrapping around the screen over and over again as the ceilings collapses. By tapping the screen, you can throw a spanner straight up, colliding with the hanging stalagtites and chipping them down a bit with each successful hit. The lower the ceiling gets, the more likely you are to crash into one of those rock outcroppings, so the goal is to keep the path clear until ceiling meets floor, then skedaddle to your rescue 'copter/hot air balloon/UFO on the outside.
Like most of the great classic Atari-age games, The Sky is Falling is a game heavily steeped in repetition (the good kind), gradually increasing difficulty, and mastery of a simple mechanic. The levels vary somewhat as you progress, but the basic gameplay remains stubbornly the same, allowing you the pleasure of amassing a gigantic high score you can boast about to your friends. And, if you ever end up in a real cave being chased by a pixellated boulder, you'll have the real-world skills needed to make it out alive!
NOTE: This game was played and reviewed on an HTC Incredible. Game was available in the North American market at the time of publication, but may not be available in other territories. Please see individual app market pages for purchasing info.