The Caesareum (sometimes spelled Caesarium) was a temple originally constructed by Cleopatra for Antony. It stood near the shore in the center of the harbor of Alexandria, and even had parks and libraries. After the fall of Antony and Cleopatra, the temple was finished by Augustus and he dedicated it to the cult of the Caesars. In the 4th century the temple became the Cathedral of Alexandria, and in 912 CE the building was destroyed.
The Caesareum was home to a couple fun deaths: it is possible that the Caesareum is the temple in which Cleopatra commited suicide by asp bite. It is definite, though, that the temple is where Hypatia, Neoplatonist philosopher, astronomer and daughter of the great mathematician Theon, was stripped, flayed, and burned alive as a witch.
Though the temple no longer stands, the Caesareum is still known for the two huge red granite obelisks that stood outside the temple (each called "Cleopatra's Needle"). The obelisks are two of nine erected by Pharaoh Tuthmosis III around 1500 BCE in Heliopolis (also called Anu), and were covered in inscriptions commemorating Tuthmosis III's third sed festival (36th year in power). Later, Ramses II added inscriptions to the obelisks commemorating his victories as well. Around 10 BCE, the Romans transported the obelisks to Alexandria to stand in front of the great Caesareum. In 1819, one obelisk was presented to the British government (but not erected until 1879) and in 1879 the other was given to the American government; they now reside near the Thames (London) and in Central Park (New York City). Today, a large statue of the Alexandrine nationalist leader Saad Zaghloul stands where the Caesareum once loomed, and ruins of the building still lie under the houses lining the sea-wall.
The word "Caesareum" also refers to a temple built for the worship of the Caesars; though the Caesareum was not originally constructed for the cult of the Caesars, its grandiosity made it the most widely known. Other Caesarea have been found in Antioch, Tadmor and Cyrene.
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References:
Mesafreen.com: http://www.mesafreen.com/Html/AlexAgamy/MonumentsGreekAndRoman.htm
Central Park 2000: http://www.centralpark2000.com/database/obelisk.html
Cleopatra's Needle: http://members.aol.com/Sokamoto31/ny.htm
Cleopatra's Needle: http://www.akhet.co.uk/cleo.htm
Cleopatra, the Last Pharaoh: http://ce.eng.usf.edu/pharos/alexandria/History/cleo.html