I hear it in a lot of songs but am noticing it more and more in everyday speech, the phrase "the reason why".
Obviously, why rhymes with a lot more things than reason does (season, teasin', pleasin' is about all you get in song lyrics these days) so I can accept the poetic licence angle but in everyday speech, the sentence "He did it without knowing the reason why." is, I'm afraid, completely unnecessary.
Can I give you a reason? Can I tell you why?
Well, I've just illustrated it: they're kind of the same thing. If you're asking someone "why?", you could just as well be asking "for what reason?". The meaning is identical. In my earlier example, it would be sufficient to leave out either option: "He did it without knowing the reason," or "He did it without knowing why,".
To use both is tautologically superfluous, yeah?
So stop using it in everyday speech. And if you're a songwriter that employs the phrase, you could really do with taking a longer look in the rhyming dictionary when you're sitting at the piano.