One thing I noticed was that the hanging occurred in operations which should have displayed an Open or Save dialog. I'll spare some of the troubleshooting operations I went through to see if the problem was related to specific application updates (the iCal update, or another update of a pre-release version of a network utility).
The solution came when I recalled a similar problem with OS 9 hanging because of aliases to recent servers in the System Folder's Recent Servers folder. So I fired up the Terminal and went to /var/automount/Network, and, indeed, found a half-dozen directories there that corresponded to different servers. After deleting these, everything worked fine.
I haven't seen this problem reported elsewhere, but it's certainly something to look for. If an application hangs when it's about to display an Open or Save dialog, it could be that the Finder is looking for those recent servers before displaying the dialog, so when you click the Network icon in the sidebar they display.

