iTunes for Windows XP can be run on Fedora 9 using Wine, an Open Source implementation of the Windows API on top of X and OpenGL. Please note that iTunes runs a bit slow over Wine and I have yet to test an iPhone or iPod with this configuration.
First, install all the wine packages.
sudo yum install wine*
Now, install the pulseaudio alsa plugin for sound support
sudo yum install alsa-plugins-pulseaudio*
Next, download the Windows XP iTunesSetup.exe from Apple.
firefox http://www.apple.com/itunes/download/
Now, install iTunes using wine
/usr/bin/wine iTunesSetup.exe
You can now run iTunes manually like so:
env WINEPREFIX="$HOME/.wine" wine "C:\Program Files\iTunes\iTunes.exe"
If you get an error regarding the registry, ignore it by clicking OK.

Here is a screenshot of iTunes running on Fedora 9.
Note that there is an icon for iTunes in Gnome's Notification Area (system tray).
For more information see the iTunes application page at winehq.org.
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iTunes 8,01 blows up during
iTunes 8,01 blows up during install when it tries to install the Bonjour service. I can't get the install to complete.