One example of Beowulf's nobility is his treatment of Unferth after defeating Grendel's mother. Despite Unferth's churlish treatment of Beowulf upon his arrival at Heorot, Beowulf acknowleges Unferth's willingness to lend him Hrunting before his battle with Grendel's mother. When he returns the sword to Unferth, he "bade Unferth take the sword and thanked him for lending it. He said he had found it a friend in battle and a powerful help; he put no blame on the blade's cutting edge. He was a considerate man" (1808-1812). Had Beowulf not been of noble character, he would not have been so gracious and modest when he returned that sword - he would probably have said something like, "What a piece of junk, thanks for nothing!"
The giving of gifts is a sign of nobility and Beowulf himself is always generous. One instance of this that struck me was that when Beowulf and his men were getting ready to leave for home, he even gave a gift to the guy who had stood guard on his boat the whole time Beowulf was dealing with Hrothgar's problems:
"The guard who had watched the boat was given
a sword with gold fittings and in future days
that present would make him a respected man
at his place on the mead-bench." (1900-1903)
One more example begins with line 2177 and runs through 2189, and is an entire section extolling the virtues of Beowulf, including the fact that he behaved with honor in battle, kept his temper, etc.
What a guy this Beowulf was!