Thunderbird, absolutely, using 2 extensions - WebMail
and Yahoo for WebMail for Yahoo and AOL for WebMail for AOL.
They also have an add-on that supports using GMail, but GMail actually allows POP access natively, you just have to go into the options and enable it, and then set up your GMail account in your client. This will work for any client that allows for Secure POP and Secure SMTP.
Cannot answer for other mail clients, though I do know that there is some software out there (YahooPOPS?) that allows you to grab Yahoo mail in most clients - but that requires running software in addition to other mail clients.