tell me which provider has an integrated single signon service for all of those above? Which provider has apps for their service for all major OS'es (including mobile), and is mostly free (or low cost)?

The cost of free is worrying about arbitrary closure, in this instance. Fastmail is much better than Gmail, for what it's worth.

Microsoft does. OneDrive for storage, Outlook webapps does email and calendar. Office online has Word, Excel, etc. All accessed with one Microsoft account. All free.

You might not want to be tied to Microsoft but Google is not the only option.

Edit: Overlooked the comment about Apps. Microsoft offers apps for mobile, but not Linux. Although even on Windows I use the browser to access the services which will work on Linux.

Microsoft's office offerings comes very close (cept for the free part - which i guess is just a bonus and not a requirement). Although i have to say, despite microsoft's attitude for keeping compatibility and old stuff working, they too could chuck a google reader one day, and deprecate/remove a needed service (along with all your data).

What's needed is a syndication of data, and inter-operable apps. Like how xmpp worked. But of course, all vendors don't like this, because it turns themselves into a commodity.

The point is to not put all your eggs in one basket. Doesn't matter who owns that basket.

apple

last i checked, icloud apps can only run on macs.