Phee-ew!
Just now the Intellisense stopped working in Visual Studio 2008. Scared me a lot - since I thought that it would make me re-install the complete Visual Studio 2008. That took me at least 3 hours to install.
But Richard Fennell had the solution and that helped me to evade that situation. Here is the solution: http://blogs.blackmarble.co.uk/blogs/rfennell/archive/2007/12/01/intellisense-not-working-in-visual-studio-2008.aspx
[UPDATED] As it turns out this was only part of the solution. The real problem was the integration with ReSharper - here is how to solve it.