It might not be the single most important part, but the fact is that most people who've played Mario will remember (and be able to hum/sing/whistle) 'that' music; not to mention some of the sound effects like collecting coins or power up mushrooms etc!
My interpretation of what happened in this thread is 1) I misunderstood FranticPanda's argument as being that SMB would not have codified the platformer genre if not for the music, 2) FranticPanda and Mecha misunderstood me as arguing that music has no power and adds nothing to any game, 3) KM advised us to stop arguing, because it was going nowhere and accomplishing nothing. I don't believe anyone has said that SMB's sound design is not widely recognizable. We can agree on that.