Earned income remains taxable regardless of age. Similarly, such income continues to be subject to Social Security and Medicare taxes (FICA for an employee; self-employment tax for a self-employed person). The one age-related break: once a worker reaches the full retirement age (currently 66), then he/she can have any amount of earned income without a reduction or complete loss of Social Security benefits.
Generally, an unmarried person who maintains a household for dependents and is allowed to compute his or her tax based on head of household rates, which are more favorable than single person rates.