Beowulf is the quintessential Anglo-Saxon epic poem for many reasons, and one of them is that is an accurate depiction of Anglo-Saxon life. Every culture has a basic set of beliefs, a philosophy, based on the things that matter to the people of that culture, and they are most easily identified by what that culture values.
One of the primary qualities the Anglo-Saxon culture valued was loyalty because they lived in a rather inter-dependent, tribal culture. When invaders came, for instance, they had to rally together to defeat their common enemy. This kind of loyalty is reflected in the poem, as well. When the Hrothgar is in trouble, Beowulf (a Geat) goes to help. No one particularly asks him to go, and the king does not keep his best thane from going on this dangerous mission. Beowulf simply
heard how Grendel filled nights with horror and quickly commanded a boat fitted out, proclaiming that he’d go to that famous king would sail across the sea to Hrothgar.
Grendel is a threat to Hrothgar's realm, and this loyalty is both necessary and rewarded.
Another quality the Anglo Saxons valued was bravery. Of course theirs is a warrior culture, a culture in which only the strongest and most able can survive. Beowulf is full of examples of this aspect of the Anglo-Saxon culture. First we have the fourteen selfless warriors who accompanied Beowulf on his mission to kill Grendel. Then Beowulf tells stories of his past exploits; to some (like Unferth) these recitations sound like bragging, but the others are reassured by these tales of victory against all odds. To them, bravery is a virtue, one they especially need at this time of Grendel's persecution. And of course we see Beowulf's feats.
A third aspect of Anglo-Saxon culture that is reflected in Beowulf is generosity. Because he expected his warriors to be brave and risk their lives when called upon, the king did not keep the spoils won in battle but bestowed them generously on his thanes. Closely tied to this is hospitality. Many times in Beowulf, Hrothgar and his wife treat Beowulf with what seems like excessive hospitality, and of course the gifts Hrothgar bestows on Beowulf after he defeats Grendel are extravagant. In turn, Beowulf generously presents a portion of his gifts back to his own king when he gets home.
The most significant aspect of the Anglo-Saxon philosophy is their belief in fate (Wyrd), and this philosophy runs all through the poem. Because no one knew their time to die and they believed their destinies were out of their own control, they were fierce warriors who lived to attain fame and glory, the only two things that would live on after they died.
For every one of us, living in this world
means waiting for our end. Let whoever can
win glory before death. When a warrior is gone,
that will be his best and only bulwark.
For example, Beowulf feels no fear before his confrontation with Grendel because he knows that his only job is to fight valiantly and fate will deal with him as it will. If he lives, he will achieve great honor and many gifts; if not, he will live on in glorious retellings of his exploits. When he is about to follow Grendel's mother into the deep, Beowulf tells Hrothgar to take care of his men and to give Beowulf's own king, Hygelac, all the treasures he has earned (lines 1480-1483). He understands that he might not win this fight, but his concern is for his men, his king, and his legacy.
What happens in Beowulf is an accurate reflection of Anglo-Saxon philosophy.