I would also want the "unread" count to appear next to the notification icon.
I use CheckGmail, it:
- Notifies on New Mail
- Previews New Messages
- Open New Messages (without a browser)
- Can Blink LEDs (I think that's cool.)
While unread count isn't part of the icon, it shows when you hover.
If you're only considering to check webmail like Gmail and you've got Firefox running anyway, then an alternative is to give the popular Firefox add-on Webmail Notifier a try.
It features multiple account checking, and also settings for displaying unread mail counts. An icon will appear in the bottom right corner of Firefox's statusbar. Left/right clicking gives you options like unread count, and opening your Gmail inbox in a tab.
Gmail Notifier Firefox extension shows the in box and unread mails information
Have look on this link http://ubuntu-tutorials.blogspot.com/2007/03/gmail-notifier-for-your-ubuntu-desktop.html