One of the things that nags me with Thunderbird is that there is no easy way to achieve a proper global inbox if you have multiple IMAP accounts. If you use the POP protocol, no problem, but IMAP is another story. One common "solution" is View -> Folders -> Unified and i think the result sucks because it just makes more of a mess of how mail folders are displayed, especially when you have multiple IMAP accounts.
While i think a true unified inbox for IMAP accounts may be in the Thunderbird pipeline, you can achieve something reasonably close with a simple message filter in the interim. Why i didn't realize this sooner, i don't know, because i've been fighting with this for quite a while.
Go to 'Tools' -> 'Message Filters' and select your first IMAP account. Create a new filter and give it a name, then select to run it when getting new mail and after junk filtering. Make sure to select the 'Match all messages' option and then in the actions area, set it up to 'Move message to' and 'Inbox on Local Folders'. Done. Do the same with the rest of your accounts.
Now when you collapse the IMAP accounts in the folder view pane, Thunderbird will just display the names of the accounts followed by the normal Local Folders tree without all the extra garbage.
Anything else you want to move to the Local Folders tree, such as Drafts, etc., you can do from the account settings.