Here is the situation: My mother has lived with me for years I have put her on my taxes as a dependent but never added her ss (which is a grand total of $600.00 a month $7500.00 a year). I made $45,000.00 this year should I put her ss income on my taxes?

No, you don't have to as ss is not taxed even if she were to do her own taxes she would not pay taxes on her ss.

OK what effect would this have on any of the stimulus checks that I have heard grumblings about?

She needs to file an information return to qualify for the Economic Stimulus Rebate, unless you already got one for her as your dependent.