Many parts of the Bible, which consist of poetry, proverbs, prophesy, laws and instructions, cannot really said to be true or false. Thus, the consideration is whether the history recorded in the Bible is accurate. For the most part, the answer is "yes". The Bible is as accurate as any history of events that happened thousands of years ago. Obviously, it is written from the perspective of one group of people, and the reader needs to consider their viewpoint, biases, and reasons for recording events when deciding which passages are believeable. This is true of any history.
The Bible records a long genealogy, from Jesus back through the kings of Israel to early leaders of the tribe. In places, this lineage can be confirmed by other histories, in others it is the only record. It is quite plausibly accurate all the way back to Adam. One does not need to accept the ideas of creationism, or the notion that Adam was the first human being, to believe that he did exist, the earliest recorded leader of the tribe that would become Israel. Like many other ancient cultures, this tribe had a long oral tradition, including a record of its ancestors and heroes that was passed down for generations until it was finally written down.
For the oldest events in the Bible, various correlations with events known from other historical and archaeological sources are really just a matter of conjecture. Perhaps the oldest of these is the Flood. Other Middle Eastern cultures, notably the Sumerian share very similar flood myths. Geologists have recent shown that the Black Seas was a small freshwater lake until the rising sea level at the end of the last ice age caused Mediterranean Sea waters to flood it sometime around 5000 B.C. Most likely, the legends are based on this prehistoric event.
One contradiction arises at this point. If the genealogy is correct, Noah did not live that long ago, so either the lineage is wrong or Noah did not really experience the flood. It may be that the flood myth was tied to his name the same way that the creation myth was tied to Adam's.
Another event that can be tied to historical and geological events is the Exodus. The fifteenth and sixteenth Egyptian dynasties, who ruled from about 1780 to 1570 B.C. came from a Semitic people called the Hyksos. When Joseph led his brothers and their families to Egypt, it was likely during their rule. Their subsequent overthrow would then be the basis of the verse "Now there arose up a new king over Egypt, which knew not Joseph" (Exodus 1:8). Under this new dynasty, the tribe of Israel were enslaved.
Around this time, a volcanic island named Santorini in the Mediterranean exploded, similarly to the island of Krakatoa in the South Pacific in 1883. This catastrophic event caused tidal waves and earthquakes throughout the eastern Mediterranean basin, and is believed to be one of the key reasons for the fall of Minoan civilisation on Crete. They could also explain the strange phenomena (raining frogs and such) recorded in Exodus as the plagues, and even account for the parting of the Red Sea. (Note that the Hebrew name Yâm-Sûph probably referred to a body known as the Sea of Reeds, a shallow, marshy body of water at the north end of what is now known as the Red Sea.)
From this time forward, there are an increasing number of other sources that confirm the Biblical account of events (for example, historical records from the various kingdoms that conquered Israel).