With HTML5 you can easily make web apps work offline with application cache. In Spotify's case the challenge is of course bigger since they would have to support offline playlists and local files first, for it to be useful.
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As olejon says, it is very possible with HTML five and the utilisation of cookies etc.; but the web player is still in beta, so not all the planned features are implemented yet. I don't work for Spotify, so I can't tell you whether it is planned, but as MikeyBoi suggested, you can submit this as an idea to the ideas thread of the community; and once it gets enough Kudos, it will be reviewed by Spotify :)
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