As others have mentioned this can be caused when some firewalls and proxies prevent access to pages containing a large amount of ViewState data.
ASP.NET 2.0 introduced the ViewState Chunking mechanism which breaks the ViewState up into manageable chunks, allowing the ViewState to pass through the proxy / firewall without issue.
To enable this feature simply add the following line to your web.config file.
<pages maxPageStateFieldLength="4000">
This should not be used as an alternative to reducing your ViewState size but it can be an effective backstop against the "Invalid length for a Base-64 char array" error resulting from aggressive proxies and the like.