iTunes represents a style of software philosophy not commonly seen on Linux for two main reasons: choice, and feasibility. In iTunes the entire package of CD-Ripping, music store, music playback, library management, syncing with remote devices, podcasts, tag editor & information fetcher etc. are all bundled into one. As a result of this people are forced to choose a single monolithic software stack or nothing.
Instead, linux advocates modularity, the capability for different software packages to swapped in and out as part of a larger work environment. This allows greater choice amongst users for what exactly they use, and it makes development easier, as any given project can focus on a smaller task. Because of this you are less likely to find a single program managing the entirety of your music collection.
The main benefit of iTunes is that using a smooth flow of different interworking programs is pretty painful in windows and OS X, but with customization you can make your entire system as easy to use as iTunes!
While it's not exactly what you requested, or even that similar I will describe my current setup, it may be informative.
I primarily use Decibel Audio Player for playback, as I like it's modal interface and simple design. For CD-Ripping I use Sound-Juicer For my library management I use the filesystem and normal file search (my tree is Music/Album Name - Album Artist/00 Track.mp3
I'm a big fan of Decibel Audio Player. It's lightweight, plugin based, and on-the-go playlist oriented. It's not like iTunes, but you'll find that linux programs don't tend to do fantastically at massive monolithic programs that do everything. In Linux you'll often have specific tools for different things like managing music on an android device and actually doing the playback of your own music. I'm not familiar with Android unfortunately so I can't recommend something for that.