Since there is no native Linux client yet, we have to use Spotify via Wine. On my OpenSUSE 11.1 (32-bit) machine, installing Wine (I got version 1.1.9) is as easy as:
sudo zypper install wine
Now, since I am using KDE 4 with PulseAudio, the step to configure Wine must be modified a bit (after Paul Betts’ hint):
Then choose OSS Driver (not ALSA Driver) in the Audio tab. Follow the other steps, i.e. closing it, run winecfg again, choose the right settings for DirectSound.
After that, download Spotify for Windows. Open Dolphin, find the download file, click on it. Wine will be automatically launched and the installation will start. After a while, you can enjoy Spotify (even with systray integration).