While Shakespeare tragedies often kill off many of the relevant characters, those left behind to lead the way into the future are interesting too. Here is a discussion of three characters who are raised to power by the end of their respective tragedies: Lucius (Titus Andronicus), Malcolm (Macbeth), and Fortinbras (Hamlet).
And, with a much pithier statement on the end of tragedies than I could ever muster, here is TheGeekyBlonde’s Hamlet, which ends with her Fortinbras summing up how Shakespeare ends his tragedies. http://www.youtube.com/watch?v=1mHQ8te8Rfk
theshakespeareminute 
I’d be interested to hear your thoughts on this subject regarding Othello. Othello’s death doesn’t shake a kingdom the way these other characters’ do, but it’s still interesting that nobody “takes his place” the way someone does Saturninus’, Macbeth’s and Claudius’.
Well, Othello’s place is technically to be filled by Cassio if my recollection serves. But it’s not as clear or built up as a power transfer.