There seems to have been an explosion lately in "audiophile" music players for Mac OS X lately. Though iTunes wiped out the need for competition when it was introduced, it has become a huge, multimedia and store program, leaving many people wanting something simpler. For a while, that was Play and one or two others, but then Amarra came on the scene. Offering higher-quality playback, it has become famous among audiophiles, alongside its biggest competitor, Pure Vinyl (and now Pure Music). As those two have fought it out in the commercial arena, the developer of Play came up with a free program, AyreWave, in conjunction with Ayre, which combined the simplicity of Play with high-quality 64-bit playback. This now leads the pack of the free players (after the association was dropped and the program re-named Decibel) if you want a simpler program and potentially better sound than you get using iTunes.
Many people feel that using the audiophile-oriented music players improves the sound with their equipment. At the very least, they offer features not available in iTunes, such as upsampling and access to the audio filters built into Mac OS X. The latter is especially useful as Mac OS X has a built-in 31-band equalizer which is very handy for learning about frequency response. However their main advantages over iTunes for improving the quality of the computer's output is a dedicated playback engine different to the one in Mac OS X or iTunes, as well as the ability to switch the system output to the sample rate of the track being played, which is important if you have a mix of high-resolution as well as CD quality music and wish to have bit-perfect output every time. Additionally, they can entirely take over the output device ("hog mode") giving the program exclusive access which prevents system beeps and other programs interfering with music playback.
So for the curious, here is a list of the players currently available that I know of, along with some basic information about them.
Amarra by Sonic Studio
Commercial, demo available for download.
Comes in three flavours: Amarra, Amarra Mini and Amarra Junior with varying features and prices. The player integrates with iTunes, or can be used stand-alone importing tracks into a playlist with one click from the Finder or iTunes. For people with a lot of RAM in their computer, it can be used in cache mode where the files are loaded into memory before playback. Includes iZotope resampling software. However, the licence either requires an iLok USB key or the software is locked to a single computer which can't be transferred.
Free, Open Source
The first player to offer a window that looks like a piece of hi-fi gear, it offers device "hog mode" and up-sampling by default. The feature list is otherwise fairly basic at present.
Integrating with iTunes, this software sits in your menu bar and feeds music via Integer Mode to your DAC. Great if you want a simple and cheap solution while still using iTunes.
Free (Open Source based on Amarok 1.4)
This multi-platform player is more of a music organiser than anything, with features geared in that direction (such as having LastFM support), rather than having any audiophile settings. Thankfully, unlike other multi-platform applications, it isn't Java based (using Qt instead), so the user interface is fast.
Decibel by Steven F Booth
The developer of Play produced a basic, high-quality music player known as AyreWave in conjunction with Ayre. This has now dropped any association with them and has been renamed Decibel. The software itself, while basic, allows one-click importing from files selected in the Finder or iTunes, "hog mode".
Ecoute by PixiApps
With iTunes integration, including song rating and metadata support, this is the player for people who want a slick, theme-able one-window interface and want to share your listening habits on Twitter, Facebook or LastFM. It also supports the Apple remote control.
Fidelia by Audiophile Engineering
With a main window that looks like a piece of high-end hi-fi gear, but far more classy than that of audirvana, it has the ability to play music directly from iTunes playlists without needing to have iTunes running. Also included are a selection of on-the-fly resampling methods, including iZotope and remote control software for the iPhone and iPod Touch available in the App Store.
Play by Steven F Booth
Until recently, almost the only alternative to iTunes if you wanted a simple music player and nothing else. Allows access to the built-in Mac OS X audio effects filters, which can be very handy if you want a 31-band equaliser, high-pass filter or the like. Since all this is incorporated into Decibel it is probably more worth it to download that instead.
Pure Music by Channel D
Commercial, demo available for download.
Based upon Pure Vinyl and using its own playback engine, like Amarra, integrates with iTunes, running in a window alongside and can re-sample music on the fly. Unlike Amarra, it requires iTunes to be running to select tracks, but offers a considerable slew of other options.
More a multi-platform internet connected media library project by previous Firefox, Netscape and Winamp developers, it might be easier to consider Songbird to music what Thunderbird is to email, yet a lot more, with online integration.
Commercial, 30 day trial period.
Designed to entirely replace iTunes, including iDevice sync support. It has, among other features Last.fm integration, watch folders, device sync transcoding rules, a duplicate finder and Airplay support.
Vox by Alessio Nonni
Free (donations requested).
Much the same as Play, a slowly developed app that does little more than just play music with a minimal footprint. Like Play, it gives access to in-built Mac OS X audio effects filters.
Since I may not be able to update this post as often as I'd like, I've now made it into a wiki/article that anyone can update here: http://www.head-fi.org/a/mac-os-x-music-players-alternatives-to-itunes