Ptolemy II ("Philadelphus") co-reigned with his father for a couple of years before taking over sole control of Egypt in 283 BC. His life was marked by controversy (he banished his first wife, Arsinoe I, and married his sister, Arsinoe II) and military expansion. Tradition gives Ptolemy II credit for commissioning the Septuagint, though his role, if any, was probably less central than that tradition suggests.
Ptolemy III ("Euergetes" — "the benefactor") ruled Egypt from around 245-221 BC, and is remembered for waging one of the wars against the Seleucid kingdom in Syria, for trying to add a leap day to the calendar, and for beginning the practice of writing massive bilingual inscriptions in three alphabets on public stelae.
Ptolemy V ("Epiphanes") assumed rule of Egypt at age 5 in 204 BC, when his father died and his father's minister Sosibius murdered his mother. Not surprisingly, the five-year-old monarch was unable to exert the kind of control of empire demands, and Egypt continued to decline. Later in life, when Ptolemy V decided he was actually a god, he continued his grandfather's practice of erecting stelae and publicized his divine ascension in the well-known Rosetta Stone. Ptolemy V married Cleopatra I, the Seleucid princess whose father was Antiochus the Great. ("The" Cleopatra is Cleopatra VII.) His rule lasted until 181.
Ptolemy VI ("Philometor") is the Ptolemy who reigned during the Maccabean revolt. Like his father, he assumed rule around the age of 5, in the year 180 BC. Unlike his father (who was managed by a series of thuggish ministers), Ptolemy VI co-ruled with his mother, Cleopatra I, until she died in the year 176. Not long after, he married his sister, Cleopatra II. In 170, his brother, Ptolemy VIII Euergetes joined him and his wife as rulers of Egypt, but the trio nonetheless lost a war to the invading Antiochus IV ("The Mad") in 168. His rule lasted until 145.
Ptolemy VII ("Neos Philopater") is an enigmatic figure who may not even have ruled at all. If he did, it was for a few months in 145, until he was deposed and then murdered by his uncle, Ptolemy VIII, who then married his (Ptolemy VII's) mother, that is, his own (Ptolemy VIII's) sister. Because of the confusion about his rule, some people don't number him at all.
Ptolemy VIII ("Euergetes II," nicknamed "Physcon" — "potbellied") ruled from 145 to 116, during which time he married his sister Cleopatra II, killed his son Ptolemy VII Neos Philopater, and then married his niece (by his wife-sister) Cleopatra III. Because of the uncertainty regarding Ptolemy Neos Philopater, Ptolemy Physcon is sometimes numbered VII, particularly in older sources; these sources therefore have different numberings for all of the Ptolemies after Ptolemy VII.
Ptolemy IX ("Soter II," nicknamed "Lathyrus" — "chick pea") reigned from 116-110, then again from 109-107, and a third time from 88-81, variously with his brother Ptolemy X Alexander I, with his mother Cleopatra III, and alone. He married his sister, Cleopatra IV, then divorced her at his mother's urging to marry another of his sisters, Cleopatra Selene. At one point he attacked Palestine from Cyprus, where he was ruling, as his mother Cleopatra IV entered Palestine from Egypt to help the Jewish regent.
Ptolemy X ("Alexander I") ruled from 110-109 and again from 107-88, when he was succeeded by his brother Ptolemy IX, who had also preceded him. He married his brother's daughter, Berenice III. When he died, Berenice was left in charge of Egypt, the first sole female ruler of that land in roughly a millennium.
Ptolemy XI ("Alexander II") was sent by Rome to rule Egypt with Berenice III, daughter and widow of Ptolemy IX Soter II. When she refused to do things his way, he had her killed, for which a mob lynched him, putting an end to a rule that had barely begun.
Ptolemy XII (nicknamed "Auletes" — flutist — and more formally "Theos Philopater Philadelphus Neos Dionysos") was the first Ptolemy to include "god" ("theos") in his title. Although his father was Ptolemy IX Soter II, his mother was his father's mistress, so his claim to the throne was dubious. He married his sister, Cleopatra V ("The Opulant"). He managed to rule with help from Rome, which produced a last will and testament of dubious providence, according to which Ptolemy XI was purported to have bequeathed Egypt to the Romans. Still unsure of his status, Ptolemy XII sided with Pompey in Palestine, and bribed Julius Caesar to pass a Roman law acknowledging Ptolemy XII as king. As a result, Egypt practically became a Roman province, and Egyptians drove Ptolemy XII out, replacing him with his queen-sister Cleopatra V together with his daughter, Berenice IV; then Cleopatra V died and Berenice IV led by herself. With more cunning and Roman help, Ptolemy XII eventually managed to return, only to murder his daughter Berenice IV. The only daughter left him was the famous Cleopatra VII, whom he named co-regent with his eldest son Ptolemy XIII.