I'm hoping this is a simple question to answer ...
How do I download an ExpressionEngine mailing list?
I can easily add emails to an existing or new mailing lists however I can not work out how to download a list (in a spreadsheet or similar).
You should be able to do this with the query module in a template (or with a query directly to your database, of course).
Something simple like this should output what you need:
{exp:query sql="SELECT email FROM exp_mailing_list WHERE list_id = '1'"}
{email}
{/exp:query}
EDIT
To improve this furher, you could use the Download Content plugin like this:
{exp:download_content filename="list.csv"}
{exp:query sql="SELECT email FROM exp_mailing_list WHERE list_id = '1'"}
{email}
{/exp:query}
{/exp:download_content}
This should make the list download as a CSV file which can open in Excel. You may need to tinker with the spacing a bit (like removing the tabs) so you don't get blank lines in the file.