What age do you pay FICA Tax?

In most cases, there is no minimum age for payroll tax withholding. Parents do not have to withhold payroll taxes on payments for services of a child under the age of 18 who works in a trade or business if the trade or business is a sole proprietorship or a partnership in which each partner is a parent of a child. Parents do not have to withhold payroll taxes for a child under the age of 21 for work other than a trade or business (such as work in the home).

There is a wage test for domestic household workers of $1,700/year (2011); individuals who pay someone less than that (including parents who employ their children) do not have to withhold taxes.

I don't find any minimum age or minimum wage test for other employers withholding payroll taxes.