Rhythmbox is an audio player for Linux that plays and organizes digital music. Inspired by Apple's 
iTunes, it is free software that is designed to work well under the 
GNOME Desktop using the GStreamer media framework.
Among the many features of Rhythmbox, you will find:
Easy to use music browser
Searching and sorting
Comprehensive audio format support through GStreamer
Internet Radio support including last.fm streams
Playlists
Display audio visualizations
Transfer music to and from iPod, MTP, and USB Mass Storage music players
Display album art and song lyrics downloaded from the internet
Play, rip, and burn audio CDs
Automatically download audio podcasts (also from iTunes)
Browse, preview, and download albums from Magnatune and Jamendo
iTunes, it is free software that is designed to work well under the 
GNOME Desktop using the GStreamer media framework. Among the many features of Rhythmbox, you will find:
Easy to use music browser
Searching and sorting
Comprehensive audio format support through GStreamer
Internet Radio support including last.fm streams
Playlists
Display audio visualizations
Transfer music to and from iPod, MTP, and USB Mass Storage music players
Display album art and song lyrics downloaded from the internet
Play, rip, and burn audio CDs
Automatically download audio podcasts (also from iTunes)
Browse, preview, and download albums from Magnatune and Jamendo
The simplicity of this player makes it awesome. Or at least more awesome than iTunes.
Rhythmbox crashes when it tries to index huge libraries of audio files (think: 100 GB+). If you must have your library indexed by your player software, try Amarok instead. I prefer audio software that does NOT index the files, that way there is no added logic, no overhead, etc. etc.
For some reason, when you first start Rhythmbox (3.4.4) , you can't see the volume control and the songs will keep playing after you close the program, two "features" I don't like and almost made me quit it but luckily both of those issues can be solved through plugins. Overall, it's a very good player and owes nothing to Clementine/Strawberry, which are the best Windows players, IMO.
Inspired by Itunes? That is NOT a good thing. The farther you get from Itunes the closer you get to common sense and reality. Itunes is horrendous. I really want MediaMonkey back, but is is such a hassle to get working on Linux.
Let's say the music on your PC is in FLAC format for max. quality. You can set Rhythmbox up so it'll do on-the-fly transcoding to MP3 (e.g.) to save space when you drag and drop files to an external player like an iPod. Super convenient, right?