It depends on the area you are in and what they will be doing. For example, in Ontario, one must be at least 18 to clean windows but only 14 to work in a restaurant.
I recommend you consult your local employment board.
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.
If I recall, it's pretty young if it's a family business. For example, let's say it's their "chores", then it's really up to the parent as to what to pay and what to give them to do.
I think as long as it's supervised by you, not endangering your child's life or limb, you can probably start them as young as they are able to write.
As @JLocke mentioned, it's best to consult someone but I think it's pretty flexible given that it's in the family business, not abusive and not dangerous.
I'm in NZ and I pay my kids to pack some orders and also vaccum the office space. They are 10 and 14. They get 20 and 40 bucks a week respectively for between an hour and three hours of work a week. The accountant tells me to keep a log of what they do so if the tax man queries it I can justify the 'expense'. I guess it's really a question for your accountant.
I have to add, my accountant told me you can't just pay them a wage and not show they have earnt it, otherwise that'll get you in trouble with the taxman.