The most compelling example of Beowulf's deeds and leadership inspiring someone is, as the previous answer indicates, Wiglaf, a young man who is not even among Beowulf's group of retainers but becomes the only one who come to his aid in the fight with the dragon. Even though Beowulf has told his troops to remain on a hill and let him fight the dragon alone, Wiglaf, not a part of Beowulf's inner circle of warriors, is inspired by Beowulf's example, and tries to shame the other warriors into helping Beowulf:
Though our lord,/the people's protector, vowed to us/that he'd do this deed along,/because he had managed the most glory,/daring deeds, of all men,/now the day is come/when our commander has need of strength. . . . (ll. 2642-2646)
The importance of this speech is that Wiglaf, a young outsider, is trying to convince Beowulf's inner circle of loyal warriors to aid him because Beowulf is "the people's protector" and he has "managed the most glory,/daring deeds." Clearly, Wiglaf is appealing to the retainers' sense of loyalty not merely to their king but also to a man who has amassed a history of "daring deeds."
Beowulf's history of defeating Grendel and, later, Grendel's mother, is sufficiently impressive to draw Beowulf's supporting warriors into the fight with the dragon and is certainly in Wiglaf's mind as he tries to convince the other warriors to help Beowulf. What inspires Wiglaf's comments, however, is perhaps Beowulf's greatest achievement, which has nothing to do with the killing of Grendel and his mother:
Thus Ecgtheow's son had survived/every quarrel, each violent conflict, deeds of courage, until that day when he had to go up against the dragon. . . . (ll. 2397-2400)
Beowulf is remembered by his people as their king, the one who, with courage and intellect, kept them free from war for at least a couple of generations. Beowulf's exploits at Hrothgar's court are impressive, to be sure, but his ability to maintain his kingdom in peace and quiet, especially in an area and era in which dynastic and territorial struggles occur on a regular basis, is his lasting and most important achievement. For example, unlike a hero Beowulf is often compared to, Sigemund, who went after a dragon for the dragon's wealth, Beowulf goes after the dragon to bring peace back to his kingdom--in the words of the poet, "that was a good king."
Beowulf's true inspiration, then, is not limited to his youthful exploits at Hrothgar's court. What inspires Wiglaf is Beowulf the king, not Beowulf the strong.
An example from Beowulf where the memory of Beowulf's deeds inspires someone occurs when Wiglaf assists him with killing the dragon in the last part of the epic. Wiglaf assists Beowulf in killing the dragon because he remembers when Beowulf was kind to him and his family when they settled among the Geats. Also, he expresses gratitude for being one of Beowulf's warriors, and understands Beowulf's need for a young, strong man to assist him, due to his age, with killing the dragon. This example shows how Beowulf's deeds of bravery and heroism not only are remembered among his people, but inspire others to deeds of heroism and bravery as well. This theme shows Beowulf's importance to his people in the epic.