Beowulf is an Anglo-Saxon poem which reflects the code of honor and action of that time. Because they believed that Fate (Wyrd) was in control of their destinies, what a man promised or swore or endeavored to do was more important than being able to do it.
This epic poem is full of actions and speeches (plot) more than character development, and the characters in the poem are defined only by what they say they are going to do and then actually endeavor to do. Beowulf says:
I had a fixed purpose when I put to sea…
I meant to perform to the uttermost
what your people wanted or perish in the attempt…
And I shall fulfill that purpose,
prove myself with a proud deed
or meet my death.
Hrothgar promises to build a great hall from which he can reward his people for their deeds, and he does it. Beowulf promises to help Hrothgar and his people defeat Grendel, and he does; then he makes a vow to defeat Grendel without weapons, which he also does. But if he had made the attempt and failed, there still would have been glory for Beowulf (and reflected glory for Ecgtheow, his king) in the effort. You see, it was the oath and the effort that mattered; the outcome of the actual battle was up to fate.
Examine Unferth for a moment, a man who does much speaking and vowing but who is considered a coward because he is a man of talk and no action. The most we ever see Unferth do is hand Beowulf a sword (offering to let his sword fight but not offering to fight himself), which would not be considered particularly valiant in any culture. He does not even try, which is what makes him a coward in this culture.
Beowulf does his exploits not because he will get a reward for doing them but because the only thing that will truly last is the glory and honor which come from making oaths and promises and then endeavoring to keep them. Even the dragon's hoard of treasure is meaningless and is buried with Beowulf.
They let the ground keep that ancestral treasure,
gold under gravel, gone to earth,
as useless to men now as ever it was.
Knowing the risks, the men of valor and honor (like Beowulf) were not reckless but willing to take the risks involved with doing honorable and valorous deeds.
At a time when courage was valued above all things, heroic men like Beowulf promised to do courageous deeds and then took action on their oaths. Whether they won a victory or suffered a loss was immaterial; fighting the battle was more important than defeating the foe. To the Anglo-Saxons then, Beowulf's last battle, against the dragon, is no less heroic than his battle against Grendel or his mother just because he lost.
In the Middle ages, chivalry will take oath-making and promises to an entirely new dimension, but for the Anglo Saxons, speaking oaths and promises (and then acting on them, win or lose) was their means of achieving honor and lasting glory.