I remember seeing Comet Hale-Bopp in 1997 - I was with a group of political activists on my way back from a day-trip to Sarajevo, and our bus pulled over on a mountainside road to let us all have a good look. And back in the winter of 1985, when I was working at Armagh Observatory, I showed people Halley's Comet through one of the larger telescopes there. But that's only thee comets that I can definitely remember seeing in my lifetime, and I am 53.
(I also remember, in the very early days of the internet, waiting for images of Jupiter after it was hit by Comet Shoemaker-Levy to come down the line. Wow, those were pioneering times.)
One can see why they were a cause of dismay in ancient times. Unlike meteors, which are there for a moment and then gone, a comet hangs menacingly in the sky, a disruptor of the natural order, changing its place rapidly from night to night. And because the tail always points away from the sun, it's always upwards form our point of view, looking like the comet is threatening to fall but not quite doing so.
Comets have been less inspiring than other solar system bodies for writers, but the SF Encyclopedia still has a decent entry. I remember reading Brin and Benford's In the Heart of the Comet many years ago. Will look out for more.