Are social security benefit payments taxed?

Of course it depends on the tax rules in your jurisdiction. For example here in the United Kingdom some forms of social payment (also called transfer payments) are included in assessable income, while others are not.

It depends on your gross income. The base amounts (tax free allowance) depends on your marital status. If your social security benefits plus your other income (from other sources) exceeds this base amount, then yes the social security benefits are taxable.