Beowulf teaches us that having great wealth, being rich, is not to be valued. What happens in the story to teach us that being rich is not important?
Perhaps the main example that "being rich is not important" is found at the end of the epic tale Beowulf.
At the end of the epic, Beowulf is dying (after a brutal fight against the dragon). Beowulf desires to see the treasure of the dragon for only one reason: he wants his people to be taken care of after he is gone. Essentially, Beowulf allows his life to be taken in trade for his people's well-being.
Over the course of the epic, Beowulf gives praise to God for everything that he has. He recognizes God's power (as seen when he is getting ready to battle Grendel and states that God will choose the victor). Time and time again, Beowulf proves his commitment to God and not to the riches which come with victory.
If the riches would have proved to be important, Beowulf would have stayed with Hrothgar. Hrothgar had promised Beowulf that he would not want for anything if he would rid Heorot of Grendel. While able to do so, the riches were not what mattered most to Beowulf (or he would not have gone home).