Along with seeking personal glory, a Scandinavian hero and king like Beowulf is expected to protect his kingdom and people at all costs, including the cost of his life. In that sense, Beowulf fulfills all the requirements of kingship in both Scandinavian and Anglo-Saxon cultures.
After the dragon, as revenge for having a piece of his gold-hoard stolen, devastates Beowulf's kingdom, Beowulf tells his warriors:
I dared many/ a fight in my youth; again as an old/protector of the people, I'll seek out conflict,/and earn some glory, if this mankiller/will come out to me/from his earth-hall.
Beowulf's speech is, in part, boastful but, more important, he resolves to fight in order to protect his people, a king's primary duty. At this point, Beowulf has lived a long, successful life as a warrior and king, and he could have, as Hrothgar did, ask for help to rid his kingdom of an enemy, but the duties of kingship to a hero like Beowulf do not allow him to ask others to protect his kingdom.
Beowulf makes this duty even more compelling when he tells his warriors that they are not to fight alongside him:
You wait on the hill, protected by war-mail,/Men at arms, to see whether one/of us two is better--at surviving his wounds/after the battle-clash. It's not your job,/nor the mandate of men, save for me alone,/to expend energy--against the monster, to do noble deeds.
We can argue, of course, that Beowulf wants the glory for himself, but given the fact that he is an old man, and he knows his limitations, Beowulf most likely saw this battle as his last. If he succeeds in killing the dragon, he not only protects his kingdom but also wins significant personal glory, and his desire to fight alone may also indicate his hope of saving the lives of all or some of his warriors--in other words, Beowulf is sacrificing himself for his people and kingdom. Nothing could be more honorable than that.
Many critics have noted that, other than Wiglaf, Beowulf's warriors failed to aid him at the end, but we have to keep in mind Beowulf's injunction to the younger warriors--do not come to my aid.