Currently Spotify only provides Debian / Ubuntu packages but it’s also possible to install it in Fedora 16. Please note that you need a Spotify Unlimited or Premium account to use the Spotifiy for Linux client.
1. Install the needed libraries.
sudo yum install qt-mobility qtwebkit
2. Create two symbolic links so that Spotify will find the right libraries.
sudo ln -s /usr/lib64/libssl.so.10 /usr/lib64/libssl.so.0.9.8 sudo ln -s /lib64/libcrypto.so.10 /usr/lib64/libcrypto.so.0.9.8
3. Next download Spotify. You can download a package that has been converted from Debian to Fedora here: http://dl.dropbox.com/u/6310099/spotify-client-qt-0.6.1.309.gb871a7d-2.x86_64.rpm (provided by meltingrobot on www.fedoraforum.org)
If you rather want to convert the package yourself, e.g. for security reasons, you can find instructions on how to do so at http://forums.fedoraforum.org/showthread.php?t=270230
4. Install Spotify
sudo rpm -ivh --nodeps spotify-client-qt-0.6.1.309.gb871a7d-2.x86_64.rpm
Spotify is now installed and you can run it via Applications > Sound & Video > Spotify or by typing spotify in the command line.
If Spotify crashes when you start it try deleting the file ~/.cache/spotify/offline.bnk.