Greek mythology is a subject that is still frequently alluded to in many forms of media today. Though the people who expressed belief in these gods and goddesses were assimilated into other cultures over two thousand years ago, their pantheon (actually a commonly used Greek word meaning 'all gods), as well as their system of beliefs, is still very well known to us today. Indeed, a majority of people to day have a better knowledge of basic Greek mythology than they do of even the basics of other mythologies, such as Norse or Celtic.
Of course, I use the term 'basic Greek mythology' to refer to both the Greek deities as well as the Latinized derivatives worshiped by the Roman Republic. Many people just term the whole group Greco-Roman mythology, but I've always felt that it should simply be referred to as Greek mythology, since the Romans assimilated the Greek pantheon along with the rest of their culture. In keeping with this, all deities will be referred to by their Greek names, with the Roman counterpart noted in parenthesis if needed.
The collection of Greek gods most commonly found in Greek mythology was termed both the Twelve Olympians or the Dodekatheon (literally twelve gods). Many of these names are familiar to those with even the least knowledge of basic Greek mythology: Zeus (Jupiter), Hera (Juno), Apollo, Poseidon (Neptune), Athena (Minerva), Demeter (Ceres), Dionysus (Bacchus), Ares (Mars), Artemis (Diana), Aphrodite (Venus), Hephaestus (Vulcan) and Hermes (Mercury). Knowing these gods and their roles is key if you wish to master the basic Greek mythology.
Zeus was the king of the gods, chief member of the Greek pantheon. His domain was that of the sky and thunder, and even today, the lightning bolt is the first thing associated with him. His spouse was Hera, queen of the gods, and the goddess of both marriage and family, and his brother Poseidon was the god of the seas, and is still never depicted without his trident.
Apollo and Artemis were twins, offspring of Zeus (though not with Hera). While both were hunters, Apollo was also the god of light, music and prophecy, among other things, while his sister was also the virgin goddess of the hunt and of all animals. Another of Zeus's children (again, not with Hera - this is a common theme throughout Greek mythology) was the goddess Athena. The patron and namesake of the great Greek city-state of Athens, she is the goddess of wisdom, defense and strategic warfare.
There is, of course, another Greek god of war, and that is Ares, whose domain is violence and bloodshed. The offspring of Zeus and Hera, his nature led him to be disliked by the other gods, save for Aphrodite. That is perhaps fitting, for Aphrodite is the Greek goddess of love, beauty and desire. In a strange twist of fate, the beautiful Aphrodite was the wife of another of Hera's children, the craftsman Hephaestus, who was as ugly as his wife was beautiful.
The domains of Dionysus and Demeter were quite intertwined - Dionysus was the god of wine and celebrations, while Demeter was the goddess of fertility and nature - the main reasons the Greeks would celebrate.
The last of the Dodekatheon - and probably the most forgotten one (at least, as a deity) - was Hermes. Hermes was the god of commerce and thieves - though it is the winged sandals he wore as the messenger of the gods that is most remembered.
These twelve Oylmpians, as well as their minor counterparts, and their interactions with each other and the mortal world form the basis of Greek mythology. Though we no longer worship them as divine, their names and domains have been remembered and referenced through the years.