Is there a way to view the CAML that is running on a SharePoint 2010 installation?
A bit like how you can monitor SQL running on a database with MS-SQL Server - is this possible with CAML and SharePoint?
Yes, to a certain extend you can watch CAML being executed by SharePoint Server. Here are the high level steps:
Make sure you select "Verbose" for event log and trace log and then save your settings
You may want to do IIS reset at this point.
Download ULS Viewer and run it
Load From ULS log in the ULS log viewer to start monitoring. Filter the log entries (Edit Menu - > Modify Filter) for condition like "Message contains CAML" so that it shows only relevant messages to you real time.
I am working on a for this at http://the-sharepoint.blogspot.com/2011/07/know-caml-queries-executed-by.html
Have a look at IDERA's tool.