Turning the Pages - leaf through original manuscripts and journals from Austen, Blake, daVinci. There's also the Sherborne Missal, the first atlas of Europe, and more. What's even cooler is you can magnify some of them, and there's audio commentary on many of them.
Beware, you need to have the latest version of the Shockwave plug-in installed before you can lose a whole day to this. :D
In all of my visits to London, I've only visited the manuscripts room at the British Library twice. When I was 14, I visited for the first time. I had just read Pride & Prejudice for the bajillionth time, so when I walked in and saw an original Austen manuscript on display, it was magical. It was the same feeling I get when I get close enough to a painting to see the brushstrokes - a transporting feeling of connection to the artist. Wow, Jane Austen's handwriting. Something she touched, owned, worked and worried over, right here in front of me. It was like a rift in time opened up and I felt like I was right there, watching the manuscript come together. Magic. That time in the manuscript room really sparked my interest in history and fascination with the creative process. And it was just so effing cool.