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There are plenty of ways a youngster can get involved in programming computers, and it need not require them to learn an obsolete computer language that nobody sane uses anymore.
"Web" languages such as Java, PHP, and especially Perl are very easy to learn, and can produce results quickly. I've taught 5th graders the basics of PHP in an afternoon. It has the advantage of being very top-down in design, English-like in syntax, and the most important of all: a useful skill in and of itself (how much do BASIC programmers make today? PHP programmers are in high demand at many "Web 2.0" houses!). Kids can create things that they can demonstrate to friends, and when they become teenagers they'll have the coolest MySpace in town.
The reason why BASIC has disappeared from modern computers? It sucks. BASIC, with it's outdated flow control structure ("GOTO considered harmful"), lack of object-oriented programming, and arcane syntax make it a very poor choice to teach computers nowadays. Professors of CompSci classes from the high-school to the graduate level are all of the opinion that BASIC did more to damage my generation's ability to program than anything else because of much of the design damage in the language.
Do your children a favor. Get them a good Perl interpreter for your platform of choice, and sit them down with O'Reilly's Programming Perl or one of the "Teach Yourself Web Programming in 24 hours" type books. They'll be creating things before you know it.
Heck, an account on a social MMORPG like Second Life's Teen grid would be more appropriate: at least there, they'd be learning an object-oriented language that's C-like in structure.
In the early 80's, there was a significant effort put in to creating "simple" programming languages for computer instruction. LOGO and PILOT are two glaring examples, Pascal is another one. Where are they today? Only the latter (Pascal) ever gets any serious discussion anymore. Want to know why?
They are obsolete languages trying to solve a problem that doesn't exist on modern computers. Web languages are simple to write in, flexible and forgiving, and are the lingua franca of many high-paying jobs in the field. But most importantly, when it's time to move on, PHP and Perl have the C++ source code available.. and what better way to learn professional programming than to hack the very programming language you learned as a kid?
Microsoft, Commodore Business Machines, and Atari never gave me that benefit...