Zeus and Hera were the king and queen of the gods. They married because they loved each other, but their relationship was difficult most of the times.
You can read more about their engagement and their wedding on the page about Hera Greek goddess of marriage. Their parents were against this marriage, so they married in secret and then they had an "official" wedding.
Of course, the question is: how come they could marry, if they were brother and sister? There is one thing you should remember, though: the gods and especially Zeus were the guardians of the laws and took care of enforcing them, but they themselves were above the laws (in fact, this is the explanation given by Ovid for this wedding: that the gods were the law in themselves. After all, the Romans also had a saying: "Quod licet Jovi non licet bovi", i.e. "What is allowed for Jupiter (Zeus) is not allowed for the oxen (the mortals)").
So maybe Zeus married her because she was the most beautiful among the goddesses and he wanted her as a "trophy" or maybe he married her because there were no prophecies about their future children, so he had nothing to fear from them.
-- Sidebar: Many fathers in Greek mythology were afraid that their children would be more powerful than they were (Zeus himself was afraid to have male children with Metis and Thetis), would take their throne (Uranus and Cronus), would kill them (Laius, Oedipus' father) or would bring destruction to their cities (Priam, Paris' father).--
Sorry for all these comments, let's return to Zeus and Hera. As the wife of the king of the gods, Hera was respected and she was the goddess who protected women and marriage. She probably was a divinity which was anterior to Zeus, a kind of "mother goddess", but the memory of this initial goddess faded away. In some temples, Hera's altar existed long before Zeus' altar was added. And sometimes Zeus was called "Hera's Zeus", as if he were a lesser divinity.
The relationship between Zeus and Hera was not at all rosy though. After the initial courtship which lasted 300 years, they got married... and the romance ended. The main activity of the two gods was quarreling, mainly because Zeus had many affairs with other goddesses and with mortal women, so Hera was awfully jealous
That's why Zeus was spending his time chasing girls and trying to hide from Hera, while Hera was trying to catch him in the act and punish the unhappy ladies. There is even a story about the Nymph Echo, whose job was to chatter a lot, so as to keep Hera busy and allow Zeus to sneak away. When Hera discovered the ruse, she took away Echo ability to speak, leaving her only the possibility of repeating other persons' words.
As you can see Zeus and Hera were quite a disfunctional family. Sometimes Hera's reaction to Zeus' affairs was so exaggerated, that Zeus felt the need to react, even by beating her! (Ouch! So much for being the queen of gods!) One day, when Hera raised a storm against Hercules' ships, Zeus was so angry, that he decided to punish her. He hang her from the clouds, tied by her wrists, with anvils attached to her ankles. The poor Hera stayed there night and day. All the other gods could hear her moaning, but none dared to help her. The only one who had the courage to untie her was her son, Hephaestus, that's why Zeus threw him in rage from mount Olympus and poor Hephaestus got crippled for life.
Sometime Hera would just leave Olympus, hoping that she would be missed and looked for. Once she left to Euboea, and Zeus didn't know what to do to bring her back (I really can't understand why he wanted that shrew back). A wise man, Kithairon, advised him to make a wooden statue, dress it like a bride and travel through Greece, telling everyone about the new girl he was going to marry. Hera heard about it and came immediately to see what it was all about. She was very pleased when she tore the veils apart and she saw that is was only a statue, not a real woman.