Shake Shingles
Basically these are split pieces of cedar of which come in different grades. Their most positive attribute is their rustic look. Conversely they rely heavily on felt to protect the roof from leaks, shakes do not carry warranties comparable to asphalt , and they are considerably more expensive that asphalt.
Slate
A very distinguished product that last a very long time used on multi million dollar mansions, churches, and castles. While beautiful this product is very heavy and roofs must be specially reinforced to support there tremendous weight. Slate roofs are also tremendously expensive for both the material and labor.
Composite Slates / Shakes
There is a large variety of composite products on the market usually they are composed of plastic resins that are molded to look like either slate and in some cases shakes. As opposed to real slate these products do not require special reinforcement to the roof and is less expensive. But they are still considerably more expensive than asphalt and some brands have been susceptible to color fading.
Metal
Commonly this product comes in sheets (standing seam) and is for the most part durable. It sheds water and snow well and resist weather conditions. Conversely it’s industrial look is not ascetically desirable to some people and while it will take the impact of hail it will also dent, similar to a car.