According to the Star-K, granite countertops, so long as they are not granite composite, which generally contains some plastic components, can be Kashered for Pesah.
The operative paragraphs are:
Porcelain, Corian or Granite composite sinks should also be considered similar to a china sink, since there is a controversy as to whether these materials can be kashered.Granite composite is a material fashioned from granite and plastic. Most sinks that look like granite are actually granite composite.
Countertops – Silestone, Porcelain Enamel, Corian, and Plastic/Formica and Granite Composite countertops cannot be kashered. They should be cleaned and covered. To place hot food and utensils on these countertops, cardboard or thick pads must be used to cover the counter. Corian is also a form of plastic that cannot be kashered, but since the chometz penetrates only a thin layer of the counter, it can be sanded down to take off a layer of Corian (the thickness of a piece of paper). It then is considered kosher for Pesach. However, only a qualified contractor should attempt this procedure. Pure Granite (not granite composite), Marble, Stainless Steel, or Metal may be kashered through eruy roschim. Wood may also be kashered through eruy roschim if it has a smooth surface.
As for glass not needing to be Kashered, that does not appear to be so simple. According to the same article, glass should only be "Kashered" via Milui Ve'Irui.
In pre-war Europe, where glass was expensive and hard to obtain, it was customary to kasher drinking glasses by immersing them in cold water for three periods of 24 hours. This is accomplished by submerging the glasses for one 24 hour period. The water should then be emptied and refilled and alowed to sit for another 24 hours. This procedure should be repeated a third time, for a total of 72 hours. This procedure of submerging cannot be used for Pyrex or glass that was used directly on the fire or in the oven. In general, kashering glasses is only recommended in cases of difficulty. Wherever glasses are readily available for purchase, special glasses for Pesach are preferable. Arcoroc and Corelle should be treated as glass for kashering purposes.