<p>Would anyone recommend a particular JavaScript charting library - specifically one that doesn't use flash at all?</p>

If you're using jQuery I've found
flot
to be very good - try out the
examples
to see if they suit your needs, but I've found them to do most of what I need for my current project.
Additionally
ExtJS 4.0
has introduced a great set of charts - very powerful, and is designed to work with live data.