The greeks had a large number of gods that they worshipped each governing its own part of the world. An interesting thing to note about the greek gods was that they were themselves created by the universe, a stark contrast to the modern view of a god as something that created the world. Of the many greek gods twelve of them were considered most important and labeled the "Olympian" gods. These were Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, Hestia, and Dionysus.
Zeus
Zeus is most well known for two things, first he was the king of the gods, and secondly he used lightning bolts as his weapon. He was the youngest child of the titans Cronus and Rhea but in spite of this became the king of the gods because all of his siblings were eaten by Cronus and lived in his stomach until he lead a rebellion against his father and saved them. Zeus' lightning bolt was actually made by the cyclops for this very purpose and is what allowed Zeus to overcome the Titans. An interesting thing about Zeus is that his rule among the gods was not actually very popular to the point where they rebelled against to at one point. In spite of this he was able to easily crush this rebellion using his lightning bolt.
Hera
Hera was the wife and sister of Zeus and queen of the gods, she was the goddess of family and marriage. She is most noted for her hatred of those Zeus had affairs with and their children. One of the most famous stories about this involves Heracles the greek equivalent of Hercules. It was said that at one point Hera drove him insane and as a result he killed his wife and children, which prompted him to seek repentance by completing his famous twelve tasks.
Poseidon
Poseidon was the god of the oceans and earthquakes and brother of Zeus. The things he is most well known for was the sinking of the city of atlantis, and keeping Odysseus at drift for many years in the story of the Odyssey.
Demeter
Demeter was the goddess of fertility and agriculture. She is most well known for working with the people to tend to farms and not really having any special powers.
Athena
Athena was the goddess of wisdom and strategy in war. She is well known as being the patron deity of Athens and daughter of Zeus. There are many stories of her birth but one of the most interesting one involves Zeus' first wife. The story says that before he married Hera Zeus was married to another woman named Metis the titan god of wisdom. This ended though when a prophecy was spoken saying that Zeus would have a child with her that would one day overthrow him as the ruler of the gods. When Zeus heard of this he ate his wife in the same manner Chronus had eaten his siblings. It is said that some time later Athena sprouted from Zeus' forehead fully grown and in armour.
Apollo
Apollo was the god of the sun, music, and the arts. The most famous story involving him is the trojan war as recorded in the Illidan. In this story he aided the Trojans in killing Achilles by guiding the arrow that struck his heel and allowed him to be killed. He was also the patron god of Troy.
Artemis
Artemis was the goddess of the hunt, archery, virginity, and the moon. She is well known for killing the greek Adonis after he boasted that he was a better hunter than her by sending a boar after him.
Ares
Ares was the god of war and bloodshed and child of Zeus. Surprisingly in spite of his being the god of war Ares was actually rather weak for a god having been defeated by mortals on several occasions. In one case he was even trapped in a copper jar a myth that some people believe may be the source of stories of a genie in a bottle. He also had a hobby of killing humans he saw as they passed by him making him disliked by many of the other gods for his bloodthirst.
Aphrodite
Aphrodite was known as the goddess of love and beauty some stories say that she was born of the sea while others put her as the daughter of Zeus. She was the wife of Hephaestus though it was an arranged marriage in order to prevent the gods of olympus from fighting over her beauty. In spite of this she was known to frequently have affairs with Ares.
Hephaestus
Hephaestus was the god of fire and forges, a well known blacksmith god and the son of Zeus and Hera. In spite of this Hera threw him off of mount Olympus when he was just born in shock of how ugly he was. As a result of this he was crippled and lost the ability to walk. Other accounts say he was thrown from Olympus because he was a cripple. He was renowned as a great craftsman and it was said he and Athena taught craftsmanship to humans.
Hermes
Hermes was the messenger of the gods as well as the god of commerce and thievery. He was the son of Zeus and stole cattle from Apollo when he was an infant which Zeus found funny. He is known for wearing winged sandals and helping Odysseus on several occasions during the odyssey.
Hestia
Hestia was the goddess of the hearth and family as well as Zeus' sister. She was well known for being the kindest of the olympians but did little as she always had to attend the hearth which is obviously immovable.