The Sorcerer's Stone

The Sorcerer's Stone is a mythical-sounding object that does two things: 1) transforms base metals into gold; 2) creates an immortality potion (the Elixir of Life). Here's what Hermione learns about the Stone from a book from the Hogwarts library:

"The ancient study of alchemy is concerned with making the Sorcerer's Stone, a legendary substance with astonishing powers. The stone will transform any metal into pure gold. It also produces the Elixir of Life, which will make the drinker immortal." (13.50)

But alchemy isn't something that Rowling made up; the idea of Nicholas Flamel using the Sorcerer's Stone (more often called the "Philosopher's Stone") is actually based in legend and fact. Here's what Rowling has to say about Flamel on her website:

Nicholas Flamel is a historical character. Flamel lived in France in the fourteenth century and is supposed to have discovered how to make a philosopher's stone. There are mentions of sightings of him through the centuries because he was supposed to have gained immortality. There are still streets named after Flamel and his wife Perenelle in Paris. (source)

In Harry Potter and the Sorcerer's Stone, the characters aren't nearly as interested in the Stone's potential for making gold as they are in its capacity to bestow eternal life. Most specifically, Voldemort desires the Stone as a means of restoring himself to his former glory – using the Stone, it seems, has far less terrible side effects than drinking unicorn blood. As Dumbledore points out, however, both riches and immortality cause nothing but problems:

"You know, the Stone was really not such a wonderful thing. As much money and life as you could want! The two things most human beings would choose above all – the trouble is, humans do have a knack of choosing precisely those things that are worst for them." (17.107)