Epic poetry usually embodies the attiudes and ideals of an entire culture. What values of Anglo- Saxon society does Beowulf reveal?
I would add to the very good points made in the existing answers that Beowulf clearly shows the importance of reputation to the Anglo-Saxons. At the end of the story, when Beowulf is cremated, his treasure is buried and becomes "as useless to men now as it ever was." Physical things, in Anglo-Saxon culture, were considered transitory; there was a strong sense that nothing could last beyond a certain period of time, with the exception of reputation.
Beowulf attempts to cement his reputation at several points in this poem. In his boasts to Unferth early in the poem, he tells stories that may be exaggerated, about his exploits fighting sea monsters, in order to justify his own greatness. In the third act of the poem, he decides to fight the dragon, despite his advanced age, in order to ensure that he will be remembered as the great warrior he once was; and, finally, he tells his story to Wiglaf on the beach as he is dying because the Anglo-Saxons placed huge value on the repetition of stories in order to prolong and preserve reputation.
We can see this also in the fact that the poem includes many digressions. These digressions are used to help maintain the attention of the audience, and to shed light upon the main story, but they also reflect the Anglo-Saxons' strong belief in continual telling of the stories of their ancestors. The Anglo-Saxons believed that by keeping alive the reputations of those who had come before, they could learn more about themselves and illuminate their own actions, as well as honoring the memories of the dead.
There are many values of Anglo Saxon culture revealed through Beowulf. First, Beowulf's culture valued strength and courage in battle. This is why Beowulf is great in his culture, he is the best fighter of monsters. He is brave and he even fights Grendel unarmed. He fights Grendel when everyone else is afraid to fight him. A second value of Anglo Saxon culture that is revealed is that of generosity. An Anglo Saxon Lord was supposed to be generous to his followers, dividing up treasure with them and giving them rings as well as ample food and drink (preferably alcoholic drink). Hrothgar gives Beowulf many gifts for his service in killing Grendel. Beowulf gives him the head of Gredel which he could have kept. Furthermore, Beowulf also gives his men, who came with him, many gifts and part of any treasure he received.
Another value of Anglo-Saxon society that we see here is honor in paying a debt. Hrothgar had helped out Beowulf's father years before. His father had killed some one and could not pay the blood money for that death so he was exiled. Hrothgar paid the debt for him, so Beowulf owed Hrothgar a debt of honor which he repaid years later by helping Hrothgar get rid of Grendel. One last value that I will mention (I am sure there are others) is that of loyalty. When Beowulf goes to fight the dragon, eleven men were disloyal and ran. Wiglaf exiles them for their disloyalty.
In addition, Beowulf goes to fight Grendel for three reasons: 1. paying his debt to Hrothgar for the kindness he once paid to Beowulf's father, 2. for fame and glory and songs that will be sung about him forever and ever Amen, 3. Because the Anglo-Saxons are fiercely loyal to family and Grendel is an enemy simply because he comes from a long line of descendents from Cain--the first man to ever murder a family member. So, we know that the Anglo-Saxons believed that murder in itself is a bad thing, but murdering a member of one's own family is unforgiveable.