I bought a Honda CRF50F for my son for his 6th birthday. I also got the 'training' wheel kit.
It's a great little bike, but my son was really too young for it at 6yo -- even though he was able to ride a 2-wheel bike at 5yo. His confidence has grown, though, and now that he's 9, he's very capable of riding the moto.
Looking back, I probably would've been better off buying a Yamaha PW50 (like Scott suggested above) or just waiting another year on the Honda. The PW50 is a great little learner bike. They're smaller and easier to handle for a 6yo kid, and they're all over on Craigslist for ~$600.
Footnote - all of the youth bikes mentioned here have speed governors on the throttle handle. Makes it easy to keep the speeds down.
Lately, I've had my eye on a Polaris RZR 170...