I can think of 2 options:
a) upgrade your yahoo account to the pay version so that you can
download your mail.
b) use a free program like YPOPs! available here: http://ypopsemail.com/
If, as you describe (which is probably not what you actually meant to ask),
you want to transfer e-mails from one *account* to another *account* without
ever involving an e-mail client then:
- Check if you can enable forwarding on your Yahoo account to send them to
your other account. That probably won't help with the already delivered
e-mails sitting in your Yahoo account but will take care of future e-mails
delivered to your Yahoo account.
- If your other account has the ability to poll other accounts, configure
your other account to yank all e-mails from your Yahoo accounts. Typically
this mail retrieve function as an account option only works with POP
accounts. You'll have to find out if your other account has a mail polling
function.