I tend to prefer separate ones, though they are all set up the same way to make processing simple.
When I worked in an office, I had one at work and one at home. Now, I have one for personal/academic work, and one for my work as a wannabe novelist (contact with agents, etc.).
I do, however, keep only one calendar.
I think separate inboxes are fine, as long as you process each one of them diligently. Technically, even if you don't have separate e-mail inboxes, you probably still have multiple "inboxes:" e-mail, physical, voicemail, your "in" folder in your work bag, etc. So having separate e-mail inboxes is just another extension of that.