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.
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.