I am 76 yrs. Old how much can I make without paying income tax ?

Age has nothing to do with income tax, but I have a feeling you mean while collecting Social Security?
You are at full retirement age so can earn as much as you want.
Younger, you have to look on the SS website for the tables showing different amounts.
When you do taxes, SS doesn't have to be counted if it's below a certain amount for married or single, which may change each year.

You DO have to FILE taxes no matter how old you are, unless your only income is SS and it's under the taxable amount.
I don't want to sound like I said 'you can earn as much as you want' and not pay taxes. Being 76 doesn't exempt you from taxes, period.

You will get a higher standard deduction.
Have a look her, Table 20-2
http://www.irs.gov/publications/p17/ch20.html#en_US_2011_publink1000259845