The App Store, so far, has seen a number of duplicate apps. One group of dupes we're seeing: dice rollers. Makes sense if you twist an old saw to say "if your input involves shaking, everything starts to look like an accelerometer." Or something.
My personal favorite for randomness is MotionX Dice. It has polish and allows you to roll one to five six-sided dice at a time. I also happen to use Dice Bag (iTunes link), but that's because my nerd blood runs deep. Still, there are plenty to choose from.
So what to do with all those dice-rolling apps? On the next page I've got a roundup of games you can play with dice. Some involve a pencil and paper for score keeping or whatnot, but all use dice as the basis for the game mechanics. Next time you're stuck in the doctor's office, don't just give your kids DizzyBee, play a "real" game with them!