The reconstriction of Shakespeare's Globe is my new favorite thing in London. If you're anywhere near here, I highly recommend popping in for a performance.
Last night I saw Christopher Marlowe's Edward the II, which was fabulous, though a bit long (3+ hours). Ignoring the electical lighting, you can easily pretend you're in old London. Very cool, especially with a mug of wine. I'd like to make it back there soon for some actual Shakespeare.