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You can access your old mail on another computer
You just need to change the option to leave a copy of your mail on the server. This way, your service provider hosts your data securely, you don't need to worry about backing-up and you can access it anywhere.

For the benefit of productivity, client applications are most useful, though with the imminent standardisation of HTML5, I predict the web-based client to be as feature-rich and fluent as Outlook.

Embedding images, sharing calendars and what-not will soon be accessible with third-party sites, but I can't see M$ developing a free, full-featured web client for the pure fact that it will not generate revenue unless it's heavily laden with advertising, which frankly puts people off and subjects them to spam, data mining and malicious content.
14th Nov 2011