It sounds to me like you have a bad switch. Is it by any chance a 3 way? (2 switches running the same light, one at the top of the stairs and one somewhere in the basement) Sometimes when one of the 3 ways goes bad it does bizarre things to the other one, things which sound pretty much exactly like what's happening to you. It's probably just a simple switch replacement.
That said, when was the house built?
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