If you contributed your own National Insurance payments all your own working life and earn a State Pension in your own right, you will keep this. In the past, many married women didn't work and thus didn't pay NI contributions from their own salaries, so had to wait until their husband's reached their retirement age before they could also receive a pension themselves, based on their husband's contributions.
Obviously if somebody remarries over the age of 65, there will be other serious things they have to consider like making new Wills, especially if the ownership of property is involved and there are children of the marriage who might be due to inherit as unless new Wills are made, the new spouse would inherit, rather than the children of the former marriage.