I'm using thunderbird with gmail imap. I have several filters setup since I receive a lot of email from several mailing lists. The notification for new mail is always lit, since I always have unread email. But I would like to restrict the new email notification to only my inbox for gmail or a specific subset of folder that I consider important. How would I do this if it is even possible?
Starting with Oneiric, the Thunderbird version shipped with Ubuntu has an add-on bundled that handles integration into the message menu. That add-on called "Message menu and Unitiy Launcher integration" provides some additional options on the General tab in your Thunderbird settings (not sure about the wording, as I'm re-translating from German here ;) ). Near the options to play a sound file when a new mail arrives and such, you can decide whether the message notification should be lit for new mails and whether to do that for every folder or just for the inbox. I don't know a solution for choosing a custom set of folders, but maybe there's an add-on out there to do that.
Edit > Preferences > When new messages arrive > checkbox "Show in the messaging menu" > change radio from "For messages in all folders" to "Only for messages in my Inbox folder"
There is a bug in the add-on launchpad asking for that kind of feature. At this time, as Henning wrote, or all email or just inbox folders. All email includes RSS feeds :(