The IMU acts as sponsor of the ICMs and maintains a fair amount of information at http://www.mathunion.org/ including a list of all past venues with online links from 1998 on (as you've already encountered). For instance, the 1998 Berlin ICM proceedings are all freely available at Documenta Mathematica's site http://www.mathematik.uni-bielefeld.de/documenta/xvol-icm/ICM.html. But that's an optimal case.
I've heard in the past that there was some movement toward scanning all past proceedings volumes, but this might not be easy due to varying copyright ownership (and costs of the project). Many but not all libraries have those volumes. It's always a problem to find a publisher, commercial or nonprofit, to handle the immediate task of publication after a Congress. In recent years most invited talks have been available on the arXiv, for instance one just posted this week by Ivan Losev on finite W-algebras. But that's up to the initiative of the speakers.
Cautionary footnote: While the ICM can be quite a good experience for those attending, the published talks don't always give helpful overviews and are often highly technical. Better surveys might be found in many places, including the arXiv and the AMS Bulletin and Notices (free online). In any case, the posted Fields Medal awards and responses are a useful resource.