Replacing iTunes on Ubuntu

Introduction
Can I run iTunes in Ubuntu (or Linux in general)?
What's the best way to manage my iPod without iTunes?
What's the best way to get music without iTunes Music Store?
Is there any way to play the songs I've already purchased from iTunes Music Store?

Introduction

I remember when iTunes first came on the scene—when my wife and I first got iPods—I hated it. The interface didn't make any sense to me. The whole program seemed to be bloated; it seemed to try to do too much. Then, I got used to it. That's what happens in software. Ideas of intuitiveness or user-friendliness become moot. It's all about what am I used to? When I first migrated to Linux (first Mepis, then Ubuntu), I dual-booted for iTunes. Eventually, I grew out of iTunes and restructured my music lifestyle to fit more with Ubuntu, and I haven't regretted it since.

I no longer have an iPod. I have a Sandisk flash player. I don't buy from the iTunes music store. Now I buy CDs again and explore legal, free download sites. I've grown to love global keyboard shortcuts.

You, as an iTunes user, may get to that point. You may never get to that point. In the meantime, here are some questions you may have as a new Ubuntu user and (soon to be former) iTunes user.

Can I run iTunes in Ubuntu (or Linux in general)?

No, you can't. People will tell you there are weird ways to get iTunes running in Ubuntu, but I've never seen anyone successfully do it. If you do somehow manage to get some version of iTunes running, it will be buggy and not fully functional. There are two helper programs—Wine and Crossover Office—that allow you to run some native Windows programs, but even those don't work. If you don't believe me, check out these pages:

Wine application page for iTunes
Crossover Office application page for iTunes

You can also try installing iTunes in Wine yourself by following these instructions: How to run iTunes on Ubuntu 8.04 Hardy Heron

If you must run iTunes, your best bet is a dual boot. This means you have to reboot your computer every time you want to access iTunes and then reboot your computer again if you want to use Ubuntu. Two slightly more convenient variations of this are running virtual Ubuntu inside Windows using VMWare (or running virtual Windows inside Ubuntu using VMWare) or having two computers and a KVM switch that allows you to quickly switch back and forth between Windows and Ubuntu using the same monitor and keyboard.

All of those are workarounds.

The bottom line is that you cannot run iTunes in Ubuntu. If you want iTunes, you need a virtual Windows environment or an actual Windows environment (or a Mac).

Your best bet is still to find a native Ubuntu alternative.

What's the best way to manage my iPod without iTunes?

There are actually many native Linux programs for managing your iPod. You can see on Wikipedia a comparison (including lists of features) of iPod managers.

AmaroK and Banshee in particular often come highly recommended from Ubuntu Forums members.

What's the best way to get music without iTunes Music Store?

In 2005, someone started a project called SharpMusique, which allowed you to buy music from the iTunes music store without the DRM "protection" on songs. Even back then, I couldn't get the program to actually work. It was buggy then, and I don't even know if it works at all now.

There are several legal ways to get music electronically.

Magnatune is a non-evil label that sifts through artists to find the best in... mainly trance and electronica (with smatterings of rock and folk). Half of the purchase price for songs goes directly to the artist, and all songs are DRM-free. You can also listen to full albums (not 30-second clips) online for free.
eMusic sells a lot of songs from independent music labels (and even a few mainstream artists). Also DRM-free. Don't know that the artists get 50% of sales, though.
Jamendo allows artists to publish their music under a free license for non-commercial use (if the artist wants to go commercial later, too, that's okay). So all downloads are completely free in every way (unless you're trying to scam money off the artist). A lot of French music, but also random other stuff. There's good French music, though. I'm kind of a pop music lover myself, so my favorites are Eva Garcia and Mel's.
Uh... buy CDs. There's something nice about having CDs. You have a full backup of all your electronic music. It's higher quality (though I can't tell the difference between CD quality and 128 bitrate for MP3). Go to your local record store... or even shop online.

For more information, including user experiences and recommendations, read these Ubuntu Forums threads:
Best place to download music?
Where do you get your music?
Legal Music Downloads
music download for Linux

Is there any way to play the songs I've already purchased from iTunes Music Store?

Not legally. When you buy from the iTunes store, you agree to their terms of service, which states:

Security. You understand that the Service, and products purchased through the Service, such as sound recordings, videos and related artwork ("Products"), include a security framework using technology that protects digital information and limits your usage of Products to certain usage rules established by Apple and its licensors ("Usage Rules"). You agree to comply with such Usage Rules, as further outlined below, and you agree not to violate or attempt to violate any security components. You agree not to attempt to, or assist another person to, circumvent, reverse-engineer, decompile, disassemble, or otherwise tamper with any of the security components related to such Usage Rules for any reason whatsoever. Usage Rules may be controlled and monitored by Apple for compliance purposes, and Apple reserves the right to enforce the Usage Rules with or without notice to you. You will not access the Service by any means other than through software that is provided by Apple for accessing the Service. You shall not access or attempt to access an Account that you are not authorized to access. You agree not to modify the software in any manner or form, or to use modified versions of the software, for any purposes including obtaining unauthorized access to the Service. Violations of system or network security may result in civil or criminal liability.

That said, if you don't care about breaking the law or the terms of service, you can probably get around the DRM by burning the DRM'ed songs to CD in Windows and then ripping the CD as MP3 or Ogg files in Ubuntu.

And, apparently, there is a program called El Tunes that allows you to play DRM-ed iTunes songs in Linux. I haven't tried it myself, and I know Apple is trying to shut the site down.