In the US there is no legal minimum age as long as it's a family business. The IRS will make a determination based on whether the work performed by the child is reasonable for their age, and the pay is reasonable for the work performed. To be clear, this only applies to your children, not other kids. (I'm sure you know this already, but I want to make it clear for others that may come across this.)
For example, it's fine to pay a 14 year-old to do simple computer data entry, but telling the IRS that an 8 year-old is doing data entry probably won't fly. To give an example of the pay issue, you can pay your kids $8/hr for a task you could reasonably pay a stranger $7/hr for. However, if you are paying your kids $20/hr for that task the IRS will likely come after you for the difference.
Unfortunately, in this case there is no hard number. It's just a matter of common sense, which can be good or bad because it gives both you and the IRS some wiggle room to argue. As long as you pass the age and pay tests you should be fine. Just make sure to keep records of everything in case of an audit.
I recommend checking out the book Tax Savvy for Small Business by NOLO. It's an excellent book, and it discusses this issue. From page 187:
Courts have okayed kids as young as seven getting paid for simple chores like taking phone messages or cleaning the office windows. Children can be paid a reasonable sum for their work; reasonable pay depends on the facts and the circumstances of each case. My advice: Don't try to pay and deduct more than a few thousand dollars per year to any of your children under age 12.