The Subject above says it all. Modern mail accounts support IMAP/POP/WebMail, and also Address Books and Calendars, with URLs and ports to log in and trade updates between server and client. This takes the idea of IMAP further, to include more of what is necessary to keep your email independent of any particular device. Automatic backup is a bonus. Also the connection can be one-way, so read-only clients can use the data through a subscription-like arrangement.
I'll say this -- both have been and are on my radar, but neither are at the top of the priority list. Both are interesting for different reasons and both are a can of worms