* Mail (often with proprietary additions, also shared mailboxes)
* Calendar (appointments, mostly: plan with others’ free/busy times, invitations, invitation replies, integration with resource booking, …)
* Global Address Book
* Tasks (To-do list, can also be mailed)
I don’t know any non-proprietary solutions that integrate all this in a decently user-friendly way. Google certainly does, but then you might as well stay with Microsoft. It’s not just about the service capabilities either: The client (be it a web or a desktop application) has to be good as well.
Another great "feature" is that if you have accounts on two different organizations, it seems to be impossible to logon to the other account even after signing out from the first account, unless you use private mode on the browser.
Check out Multi-Account Containers if you're using Firefox. They solve this exact problem.
firefox -ProfileManager or firefox.exe -ProfileManager
All your problems solved, and even others you didn't expect you could ;)
I guess gmail/google calendar can play in this space, but are there any open source options?