If you do have granite worktops in your kitchen, I am jealous. We are still in the market for a new work surface in the kitchen, and granite or similar hard surface is high on the list of possibilities.
Granite is a compressed once-molten stone formed under the earths surface. It is a great kitchen work surface because it is hard to scratch and mar stone. It is a surface you can set a hot pan on without worrying about whether it will discolor or even melt the surface. It is a surface you should be able to cut with a knife on, though I don't think I'd do this all the time because it will dull the surface of a good knife. I'd still use a cutting board most of the time. But if you do so very occasionally, you don't have to worry about cut marks in the surface of your counter.
Granite surfaces should be very easy to keep clean as well.
Not only is it a practical surface, but it's one that is appealing to the eye. One that can be purchased with a nice polished shine to it, and there are a variety of colors..personally, I would go for natural earth tones, as this is what I love, living in a log home in the country as we do.
I do love the idea of a stone surface like this, and will let you know when we finally settle on the counter top of our dreams, granite or otherwise. I hope to have a picture to share.