Mugglenet just found a list of brief deleted scene descriptions on the British Board of Film Classification’s website that will appear on the upcoming Harry Potter and the Half-Blood Prince DVD.  They are:

Harry and Hermione walk through Hogwarts hall (26 seconds)
Harry and Hermione discuss Marauder’s Map (1 minute)
Harry, Ron, and Hermione discuss the Vanishing Cabinet (1 minute, 4 seconds)
Harry and Dumbledore arrive at cave entrance (38 seconds)
Harry and Dumbledore leave cave (19 seconds)
Clouds gather over Hogwarts as Flitwick conducts choir (1 minute, 39 seconds)
Harry joins Ron, Hermione, and Ginny in the Common Room (40 seconds)
Harry and Hermione discuss Ron at Astronomy Tower (42 seconds)

So in other words, a lot of Harry and Hermione, with an extended Harry/Dumbledore cave sequence.

Interesting.  The finished film already had a lot of Harry-and-Hermione-being-good-friends scenes, which I thought was a nice touch that had been under-explored in earlier movies.  I’m surprised that there was even more.