When I was a boy, I would troll the beach with a magnet tied to a long string, hoping to snag a torn-off bit of the cosmos in the form of an iron meteorite. As an adult, I found out that if you want one, you can just buy one. This one is from the Gibeon fall, a meteor that broke apart over Namibia in prehistoric times. It was originally part of the iron core of an asteroid that later broke up. Its melted, pitted exterior marks its fiery passage through the Earth's atmosphere, but its inner crystalline structure has not changed in 4 billion years. To me, it is the equivalent of a medieval relic, a connection to the universe and its creation.
One of the holiest relics of Islam (and its predecessors in Arabia as well) is a meteorite embedded in its central shrine at Mecca. One legend has it that this stone, too, dates from close to creation, falling at Adam's feet and subsequently discovered by Abraham.
The Hall of Meteorites in New York's American Museum of Natural History has an excellent exhibit (virtual and physical) on meteorites.