Paddington Tube station on the Circle and Hammersmith lines is closed on Saturday. Other shutdowns this weekend include a portion of the Northern Line both days and some disruption on the Jubilee line on Sunday.
There are also disruptions on Docklands Light Rail, London Overground and London Tramlink. See map in the above link.
By mid-July, the Tube should be ready for the Olympics. From then on, only Waterloo and City appear slated for Sunday work thru the summer. Here is more on the long-term picture.
You can also now get updated London transport info on Twitter. Check out the link and add to your mobile!