According to efile.com, the amount of money a person can make without filing taxes depends on filing status and age. For tax year 2013, a single person under 65 years old had to make in excess of $10,000 before filing taxes, while someone over 65 years old needed income over $11,500 to file taxes. Dependents have a lower tax filing threshold of $6,100 if they're under 65 years old, single and not blind.
Turbo Tax notes that people over age 65 who receive Social Security income may be able to earn a larger amount of income before filing taxes than other taxpayers because Social Security benefits are tax-free. The single exception to this rule is if someone is married but filing separately. In this case the Social Security income is used to calculate gross income. Efile.com notes that unearned income, such as gifts or investment income, may cause a dependent to have to file taxes, even if income from work does not exceed the threshold. For example, a single dependent under 65 who is not blind had to file taxes in 2013 if that person received more than $1,000 from an investment. A single person 65 years old or over who is blind would have had to receive more than $4,000 in unearned income before needing to file federal taxes.