Last night I went with a group of friends to see a production of Hamlet which, I noticed, had eliminated references to Fortinbras and Norway (I can't imagine why). After the play had ended, I was explaining how Fortinbras represented a threat to Denmark as the tragic loss of the line of succession meant Denmark was now easy pickings for a revenge-minded heir to Norway's throne. As we were discussing the idea of Fortinbras being a threat on the horizon rather then a vivid threat (English nerds? Yes we are!), the parallels to the end of Beowulf struck me. After [spoiler alert] Beowulf is killed fighting the dragon, his people begin to weep at the thought that they are unprotected from the threats that live on the horizon. After Hamlet and pretty much everyone else dies, Prince Fortinbras shows up and pretty openly states that his claims to Denmark are now essentially unopposed (except by Horatio, who sidesteps the issue).
So my question is: would Shakespeare have been familiar with the text of Beowulf? Or even perhaps have heard it as an oral history? Would he have known of its existence at all? I've read up a bit on the manuscript that survived, and it seems that there exists an overlap of the Nowell Codex and Shakespeare's life; additionally, if there were anyone familiar with the story of Beowulf at the time, it'd be Shakespeare.
No, most certainly not. Beowulf was forgotten did not get printed until 1815. But it is very possible that Saxo Grammaticus was well acquainted to the conventions of a Germanic saga or to the saga about Beowulf itself. His Hamlet story is, after all, just another saga from the prehistory of the Danes. There are legendary figures mentioned both in Beowulf and by Saxo Grammaticus.