My kids each have three accounts: a 529, which is invested in an age-adjusted fund (it starts out agressive, and then gets less and less so as the kid approaches college age); a Coverdell Education Savings Account, which is invested in indexed mutual funds; and a custodial account.
The custodial account is for money gifted to them by friends and relatives (all gift money goes into the account), plus any amount from their allowance they wish to save.
In the custodial accounts, the kids (age 6 & 10) are allowed to buy any stocks or funds they wish. Right now, my 10yo is holding a portfolio of Best Buy and Amazon.com, her two favorite stores. She used to hold Build-A-Bear, but got tired of losing money in it, and sold it. My 6yo has stock in her auntie's company, because she likes her auntie.
As might be clear, I think it is important to teach kids about money and saving and how markets work. My parents never told me anything about money, and it took better than half my life to figure it out on my own. I think I'd be a lot wealthier today if I had gotten an earlier start.