While the actual personification of death in Greek mythology was Thanatos, the twin brother of the sleep god Hypnos, the more famous Greek figure associated with death is Hades. While Hades' rule over the world of the dead leads to some modern association with Satan (in Disney's Hercules, for instance, Hades was portrayed as a duplicitous schemer), he's actually quite different. While widely hated and feared, and certainly one of the most dour and unpleasant of the Olympians, his attitude seems to derive more from his bleak surroundings than from an evil personality. And while he often takes on an antagonistic role, this isn't always the case. In some versions of the Perseus myth, for instance, he loans his famous cyclops-made Helm of Darkness to the hero for use in killing Medusa. The Greek myth-makers often seemed to think of him as someone who, while fair and skilled at his job, really didn't like it. The story has it that Hades and his brothers Zeus and Poseidon, after winning control of the world from the Titans, drew lots to divide up the place. Zeus took the sky, Poseidon the seas (he was second to choose, but got his first choice anyway), and Hades was stuck with the underworld. The upside to this dreary position was that Hades technically owned all the wealth to be found underground, hence his alternate name Plouton, which became the Latin Pluto. I remember when the Disney movie came out, and someone asked why Hercules had his Latin name while the gods all went by their Greek ones, and someone joked that calling them by their Latin names would have meant Hades being Pluto, who of course is someone else quite different in the Disney universe. Actually, the Romans also referred to the god as Dis Pater and Orcus, but would your average movie-goer have known this?
The most famous legend of Hades is probably that of his abduction of Persephone, the daughter of his sister Demeter. (The gods never seemed to have a problem with incest; Rick Riordan's explanation for this in the Percy Jackson series is that they lack DNA.) Demeter enlisted the help of Zeus and Hermes in getting her daughter back, but since Persephone had eaten six pomegranate seeds, she was required to stay in the underworld for six months of the year. This is apparently why the seasons change, although the tilting axis might have a thing or two to say about that.