Just recently the International Mathematical Union (IMU) put online all the previous proceedings on the ICM's!!! Here: http://www.mathunion.org/ICM/ . This webpage is based on joint work by R. Keith Dennis (Ithaca) and Ulf Rehmann (Bielefeld). So you can read for free all the articles (Including Hilbert's famous problem paper; Martin Grötschel
demonstrated it at the opening ceremony of ICM 2010). I dont know when the proceedings of ICM2010 will be added. UPDATE: the 2010 articles have now been added!
As for the talks themselves there is a page with all the ICM 2010 plenary talks here http://www.icm2010.in/from-the-venue/online-streaming-archives links for videos from earlier ICM's (plenary talks and other events) can be found here http://www.mathunion.org/activities/icm
Update (August, 6 2014) Many (46 for now) of the ICM 2014 proceedings contributions are already available on arXiv, via this search. (I got it from Peter Woit's blog.) Videos of lectures can be found here.
Update (May 2014): Starting 1992 there is also every four years the European Congress of Mathematics (ECM) that the European Mathematical Society (EMS) is running.
The proceedings of the first three ECMs are now freely open. These volumes are available at
(Digitising the proceedings of the first three ECMs, published by Birkhäuser was a task carried out by the EMS Electronic Publishing Committee.)
Starting with the 4ECM (2004), the Proceedings are published by the EMS Publishing House. The EMS decided to make them freely available online too. I expect that this will happen soon and I will keep you posted. Further update (June 2014) The ECM Proceedings are now available on http://www.euro-math-soc.eu/ECM/! I was told that in a few months, the EMS will put also the 6ECM volume.