One of the most pervasive themes in Beowulf--often overlooked because it is not as dramatic as the fight of good against evil embodied in Beowulf's struggles with Grendel and his mother--centers on the nature of kingship, specifically, good kingship as opposed to disastrous kingship.
Among the digressions in the poem are several that are designed to instruct Beowulf in his duties as leader of the Geats. In lines 875-900, for example, the poet discusses the positive example of Sigemund, who, like Beowulf, kills a dragon. Sigemund's deeds and kingship are set in opposition to Heremod, a king who is described as "to all his princes, a problem for life" (l. 906) because he not only coveted riches and withheld gifts from his supporters but he also persecuted his own people. The positive example of Sigemund, who wins riches but distributes them to his retainers, and the negative example of Heremod, who betrays his own people, are meant to instruct Beowulf when he is still in the formative years of leadership.
That Beowulf absorbed these lessons is made manifest in his last act as king of the Geats in which he goes after the dragon who has been awakened by a thief. Beowulf is not interested in the dragon's hoard in order to enrich himself and his retainers. Rather, his goal is to stop the dragon's depredations against the Geat people, and Beowulf knows instinctively that this battle will be his last. His duty as king, however, is greater than his personal safety or a few more years of a quiet life, a lesson he learned when he was at Hrothgar's court as a young and untested leader.
Many different themes exist within Beowulf, and one could argue that any one of them acts as the most important or universal theme. (The basic definition of a universal theme is a theme which is shared between numerous stories, yet the stories are completely independent of one another.)
The main themes of Beowulf are fortitude/wisdom, glory/treasure, fate/providence, loyalty/vengeance, and good over evil/good verses evil. These themes stated, the most universal is good verses evil.
Throughout the text, Beowulf (representing good) battles against evil (represented by Grendel, Grendel's mother, and the dragon). Beowulf (supported by God and aligned with light) fights against the forces of evil (God-haters and figures of darkness). Given that Beowulf always finds success in his battles against evil, the theme of good over evil is readily evident throughout the text.
Although many of the attitudes, circumstances, and cultural environment seen in Beowulf reflect specific aspects of early medieval Anglo-Saxon culture, the poem possesses several themes that are typical of heroic epic.
The first common epic theme is linking physical and moral prowess. The hero Beowulf is equally strong in leadership, ethics, wisdom, and physical strength. While this conflation of physical and mental gifts is not something that is necessarily true outside literature -- one can be physically strong and a bully or physically weak and a great leader -- it is a very common feature of epic.
The second universal epic theme we find in Beowulf is that good will always triumph, no matter the odds against it. Like the association of physical prowess and morality virtue, this is based on the notion of divine providence, that God or the gods bestow gifts on the deserving and arrange events so that those they favor win.
This notion that physical prowess is a divine gift that should be used in service of virtuous causes is exemplified in the following description of Beowulf:
So Edgetho's son proved himself,...not killing his comrades
In drunken rages, his heart not savage,
But guarding God's gracious gift, his strength
Using it only in war, and then using it
A third theme is the obligation of the ruler to his people. In epic, rulers are not tyrants. The gods support lawful rulers as in a sense deputies for divine justice. The ruler is as much a servant of the gods and his people as someone who benefits from a position of power. Thus, Beowulf proves his true greatness as a king when he fights the dragon, knowing that he will die in the battle.