Is there any confirmation of Biblical events from written sources outside the Bible?

The most documented Biblical event is the world-wide flood described in Genesis 6-9.  A number of Babylonian documents have been discovered which describe the same flood.

The Sumerian King List:

Lists kings who reigned for long periods of time. Then a great flood came. Following the flood, Sumerian kings ruled for much shorter periods of time. This is the same pattern found in the Bible. Men had long life spans before the flood and shorter life spans after the flood.

The 11th tablet of the Gilgamesh Epic:

Speaks of an ark, animals taken on the ark, birds sent out during the course of the flood, the ark landing on a mountain, and a sacrifice offered after the ark landed.

The Story of Adapa:

Tells of a test for immortality involving food, similar to the story of Adam and Eve in the Garden of Eden.

Sumerian tablets:

Records the confusion of language as we have in the Biblical account of the Tower of Babel (Genesis 11:1-9). There was a golden age when all mankind spoke the same language. Speech was then confused by the god Enki, lord of wisdom. The Babylonians had a similar account in which the gods destroyed a temple tower and "scattered them abroad and made strange their speech."

Recorded on the walls of the Temple of Amun in Thebes, Egypt:

Campaign into Israel by Pharaoh Shishak (1 Kings 14:25-26),

Recorded on the Mesha Inscription:

Revolt of Moab against Israel (2 Kings 1:1; 3:4-27),

Recorded on the palace walls of Sargon II, king of Assyria:

Fall of Samaria (2 Kings 17:3-6, 24; 18:9-11)

Recorded on the palace walls of Sargon II, king of Assyria:

Defeat of Ashdod by Sargon II (Isaiah 20:1)

Recorded on the Taylor Prism:

Campaign of the Assyrian king Sennacherib against Judah (2 Kings 18:13-16)

Recorded on the Lachish reliefs:

Siege of Lachish by Sennacherib (2 Kings 18:14, 17)

Recorded in the annals of his son Esarhaddon:

Assassination of Sennacherib by his own sons (2 Kings 19:37).

Recorded on the Tablet of Nabopolasar:

Fall of Nineveh as predicted by the prophets Nahum and Zephaniah (2 Kings 2:13-15)

Recorded in the Babylonian Chronicles:

Fall of Jerusalem to Nebuchadnezzar, king of Babylon (2 Kings 24:10-14)

Recorded on the Babylonian Ration Records:

Captivity of Jehoiachin, king of Judah, in Babylon (2 Kings 24:15-16)

Recorded on the Cyrus Cylinder:

Fall of Babylon to the Medes and Persians (Daniel 5:30-31)

Recorded on the Cyrus Cylinder:

Freeing of captives in Babylon by Cyrus the Great (Ezra 1:1-4; 6:3-4)

Recorded by Suetonius:

Forcing Jews to leave Rome during the reign of Claudius (A.D. 41-54) (Acts 18:2)

Recorded by Josephus, Suetonius, Thallus, Pliny the Younger, the Talmud, and Lucian:

The existence of Jesus