It is now possible to acknowledge receipt of any new email in your Yahoo account without opening your browser and logging in to the website. Yahoo! Mail Notifier, an add-on for Mozilla Firefox, notifies users when new messages arrive in their Yahoo mailbox.

Note: it seems that the software hasn't been updated for several years - the version linked to this page is the latest to exist.

What are the key features of Yahoo! Mail Notifier?

Yahoo! Mail Notifier is featured with a small tool that notifies users of new incoming emails in their Yahoo mailbox. The name of the sender, subject, and some part of the text can be seen from the interface of this add-on.
This add-on supports Firefox from 0.9 and up. Moreover, it can also support Flock, Mozilla Suite, Netscape (8 and 9) as well as SeaMonkey (1.x and up). It is compatible with Windows platforms and can be configured with multiple accounts.
Yahoo! Mail Notifier also supports email scanning and removal can be done without starting the session. Yahoo! Mail Notifier is quite easy to install. Over and above, the installation can be done for multiple users on the same computer.