Icedove (thunderbird) with multiple accounts - different inboxes?
 

I have 2 email accounts in icedove and all incoming messages come into same inbox. I remember that some time ago they did come in different folders, am I right? Is it even possible and how?

In the Server Settings for each account there's an 'advanced' button near the bottom of the dialog (kind of a bad location for it; at first I thought it was associated with the 'empty trash on exit' setting nearby). There you can choose whether to download to separate inboxes or a single global inbox.