Right gang, now that we've got our own forum I think it would be good to put together a list of things to see and do in London, as much for those of us who live here as those just visiting.
Here's a few things for starters:
Timeout's Thigns to do at Lunchtime for less than £10
The Independent's top 50 free activities in London
Getting specific, there are several museums that you can visit for free:
The British Museum
The Tate Modern
The National Portrait Museum