Credit:
While it stops short of the Facebook Connect or Twitter integration we're used to seeing (eg. during the Obama Inauguration), C-Span's integration of the live blogging tool CoverItLive allows them to post minute-by-minute updates on developments, in addition to providing links to further coverage on blogs and news sites. At the time of writing, over 9,000 people are watching the live stream.
For those looking for a more social experience around the hearings, you can append your Tweets with the hashtag #Sotomayor and follow updates from the Twitter community by searching for that hashtag.