Tree Style Tabs looks like it has a potential to allow querying HTML via SQL. I have been thinking about this for a while. I do not have a concrete idea for an application, but it would be cool to retrieve titles of all open sites in certain group/tree. Almost like some sort of scraper.
I had similar thoughts recently. This kind of hierarchical and persistent 'view' into a graph (the web) could possibly be useful in other contexts (perhaps even as a general computer interface), and not just for graphs but generally as a hierarchical scratch board for queuing and structuring tasks and information. I'm thinking about implementing this in an experimental package for Emacs.
As for existing things, I've found Tab Counter quite useful in combination with TSTs.