The test results you have selected are very old and may not represent the current state of Wine.
Selected Test Results (selected in 'Test Results' table below)
What works
Searching and playing music, and facebook integration (with a dll override: see other comments).
What does not
Nothing I tested seemed to fail. I never did install Windows Media Player, so I strayed away from pressing the "Windows Media Player" option in the left sidebar.
What was not tested
Creating playlists and features only available as a premium user.
Additional Comments
To keep the application from crashing for accounts with facebook integration, obtain winhttp.dll, dump it in wine's system32 folder and add a dll override for spotify in winecfg.
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Native client
by Tobias on Friday December 2nd 2011, 6:15
I'm not sure if it's intended, their website states otherwise, but my Spotify Free Account also works with their native linux client:
www.spotify.com/dk/download/previews/
facebook integration broken, even with "winhttp.dll" hack
by Steve on Friday November 4th 2011, 1:02
ubuntu 10.04 using wine 1.3.31 from the wine ppa, downloaded winhttp.dll from a site via google, copied to the system32 folder, created an override, and still crashes. remove spotify from facebook and no crash.
Working setup
by Michael Olson on Tuesday October 18th 2011, 19:32
OS: Ubuntu 11.04 (wine 1.3.28)
I installed PlayOnLinux, installed Spotify using that, did the winhttp.dll hack. This made the initial Facebook-related crash go away, but had an issue of the entire program dying about twice an hour, sometimes during playback and sometimes while paused.
To fix that, I used PlayOnLinux to install wine version 1.1.27 and use it just for the Spotify setup, and configured it to use ALSA sound (on a system which uses the default pulseaudio setup). This gets me to the point where the program no longer crashes randomly. It shows a crash dialog when starting, but continues just fine once that is closed. Notification of songs to Facebook does not work, but most else does.