There is no age when you stop paying taxes. As long as you have taxable income, you are taxed. There is an increased standard deduction for persons over age 65 and/or blind.
The standard deductions for 2018 are:
Married Filing Jointly $24,000
Head of Household $18,000
For those taxpayers who are 65 and older or blind, add another $1300 for each condition.