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Davmail can get you most of the way there for Exchange. Definitely a product I would buy if it were commercialized.

I manage my email in emacs, though it's delivered to the Exchange server at work. I deliver it to a local maildir with fetchmail, and use notmuch to index it. Searching is better and faster than GMail IMO.

There's actually a surprising number of CLI implementations of popular protocols out there. I recently started using Hangups (https://github.com/tdryer/hangups) for Hangouts. And there's one for Play Music too although I can't recall its name at the moment.

Only thing I'm really, really missing now is a CLI for KeePass, but I'm considering writing one myself in Go, since I've been looking for something to do for practice in Go anyway.

Check out Davmail (http://davmail.sourceforge.net/). I use this with offlineimap to run mutt with an Exchange installation; apart from calendar invitations, it works quite well.