Bux
Free
If you're anything like us you probably find the idea of trading on the stock market slightly intimidating, but Bux eases you in and alleviates that fear by turning the whole thing into a game, literally.
Rather than trading real money you can start out by using 'FunBux' - an in-game currency which you start with 1000 of and can use in place of real money to trade and invest in real stocks, currencies, commodities and indices.
This is the real stock market, so however many FunBux you make or lose is exactly the amount of real money you'd have made or lost.
Bux isn't the only stocks app to offer virtual currency, but it also simplifies the whole process, with a slick interface and explanations for every screen, so you can easily learn the basics, along with articles written for the app which highlight the latest happenings in the stock market.
It's fun just to play as a game, but if you're feeling brave you can graduate to using real currency and try to make your millions. At that point you should probably stop treating it as a game.