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Here's a proof of concept patch that adds a 'fullstack' option to print_exception. The problem with this concept is what happens when you use it on an exception caught at the top level of a module. I'm not entirely clear on why tracebacks work the way they do, so I don't know how to fix that case (it's also late, maybe in the morning I'll be able to figure it out :)
Writing unit tests for this may also be a bit tricky.
I'm raising the priority to normal because I think this would be really useful for logging, as pointed out by Thomas.