Happy days, there's a new setting in SharePoint 2010. This one caught me by surprise though, because it stops the entire site collection being indexed.
In the site collection settings under the "Site Administration" setting, there's an option called "Search and offline availability" which contains a switch that seems to be disabled by default for certain templates (eg for the "Blank" site template, "Search Centre" or "My Sites"). If you are getting messages in the Unified Logging Service on the SharePoint Servers that looks like "This item and all items under it will not be crawled because the owner has set the NoCrawl flag to prevent it from being searchable", then go into Site Settings –> Site Administration –> Search and Offline Availability for the site in question and set the "Indexing Site Content" switch to "Yes"
Easy to fix, hard to find – all of the other search controls for a site collection are located under the "Site Collection Administration" setting, but this one – and ONLY this one – is tucked away under "Site Administration"…
Ah well. At least the problem's resolved and I don't have to investigate what might have been a configuration problem with FAST :)