I have a light on the ceiling and two switches each at opposite sides of the room to control the light. The switches have worked fine for 20 some years but now the one switch when off will not let the other switch turn the light on. I have replaced both switches but still have the same problem. Any ideas??

Either one of the new switches is bad and/or they got rewired wrong.

I agree with tkrussell.
It sounds like 1 switch went bad and when they were changed 1 or both got wired wrong.
If that is not the case than 1 of the new switches is bad.