Beowulf has been around for so long and continues to be read for several reasons.
First, the poem provides excellent insight into Anglo-Saxon life and beliefs. In this way, the poem is interesting from a historical perspective.
Second, the poem also discusses universal themes such as life and death, good and evil, and sin and redemption. The people in the poem are unsure of an afterlife and belive fame to be the only immortality. Their quest for fame makes them not so different from many people today. Thus, even though the poem is about 1000 years old, it easily connects to modern readers.
Next, Beowulf is an interesting hero, who is proud but not arrogant -- before fighting Grendel, he knows he might die and says, "Fate will unwind as it must." Modern readers love stories about heroes, so it is not surprising that Beowulf is still read today.
Finally, the poem is a great tale of adventure featuring epic battles and fearsome monsters. The story reads more like a modern movie, yet another reason why the poem is still popular.
Ultimately, there are several reasons why Beowulf is still read today.