When talking about Amarok, it's important to start with KDE. Amarok was developed on KDE-dependent distros as a more fully-featured alternative to programs such as Rhythmbox. Now, many of the KDE-dependent distros include Amarok as its default player, and Amarok has since moved on to a variety of other distros. Keep in mind, however, that non-KDE based distros will have to download a fair amount of the KDE packages for Amarok to work properly.
K/ubuntu's 9.04 release “Jaunty Jackalope" is one such distro running Amarok 2 as its default music player. This is the most fully featured and stable version of Amarok available: highly recommended.
Fedora also has a very functional, very stable version of Amarok available for download. If you're using Fedora 8 or even earlier versions, you'll end up with the older version of Amarok. However, with Fedora 9 and beyond, Amarok 2 will be available to you as well.
Pardus, another KDE-based distro, also features a reliable version of Amarok 2 as its default player.
Both SUSE and openSUSE's respective versions of Amarok does not have much by way of support. To use Amarok with either of them, it appears that you are required to be using the KDE desktop. Both SUSE and openSUSE follow the same installation procedure for Amarok.
Ark Linux also requires that you use the KDE desktop in order to use Amarok—which is default anyway. It appears to have decent support, easy install and few complaints by way of excessive bugs.
For Amarok on Arch Linux, there is plenty of support for the new version of Amarok. There is also a relatively easy way to get the older version of Amarok on Arch Linux, if you're so inclined. There doesn't appear to be too many complaints about use, though admittedly there isn't exactly gigabytes of user feedback out there.
Gentoo has had some controversy surrounding its Amarok use. In addition to a somewhat complicated web of processes that may or may not surround your Amarok installation on Gentoo, depending on what you've done as far as customization is concerned. There have also been issues of security raised about Gentoo's version of Amarok with regard to the creation of insecure temporary files that may be taken advantage of to compromise the user's entire system. Theoretically, however, these security issues have been addressed.
Mandriva allows for users to install Amarok 2 just fine. The latest versions of Mandriva use Amarok as a default music player, which is just fine by most users, though there have been some complaints about including a beta version as default in an otherwise stable system.
For Debian, Amarok is every bit as available for install. However, there are some concerns. Not all the versions are stable—the old versions of Amarok are only stable in Lenny, while the others are variously testing, very unstable, or just never going to be updated. For Amarok 2, it's mostly still in the highly experimental stage, with little or no support for the different variations.
With the massive diaspora of Linux distros out there, there's no way to develop an Amarok version suitable for every single one—nor to review them all. For more information on other Linux distros that Amarok may be used with, check out the official list. Keep in mind, however, that Amarok is not as well supported on these: you may be using an older version of Amarok, even down to the 1.3s, or using elaborate workarounds to get it working. Support is also not as good for such distros, though users may be somewhat used to that by now.