CloudPlay (http://cloudplay.fm) is a minimal music player for your menu bar. It searches iTunes of course, but also online sites like YouTube, SoundCloud, and bunch of others. Depending on the type of music you listen to, it might be all you need.

Disclaimer: I am the developer of CloudPlay.

Best one I'm aware of is Enqueue (http://www.enqueueapp.com/)

It looks like a great music player, but it's missing some Apple proprietary features. Things like Airplay, Podcasts, iPhone syncing, and anything else that couldn't be implemented in software sold through the App Store. I don't know of anything that can do those well except for iTunes, but I assume the feature bloat is part of why you're looking for an alternative.

EDIT: There was a discussion here when its free beta was released. http://news.ycombinator.com/item?id=3207736

If the music you want to listen to is already organized well you can always make playlists with Play, http://sbooth.org/Play/, drop the folders on a playlist window, set it to Repeat All, and rock on. This can help me concentrate: I don't need to star any music, nor check how many plays a song has and whether it will knock another out of my Top 25 list, and I don't get tempted to start mix and matching across genres, thereby distracting from work. I simply put all my Van (as in Morrison, not Halen), or Smashing Pumpkins, or Smiths, etc, into a play list and work.

Spotify is a bit snappier , and you can load your own local music through it. One thing I don't like though is that there is no EQ settings (at least that I'm aware of). I imagine they will probably eventually add that feature. If you don't mind having the option to listen to a whole slew of other music (with ads). I believe ads don't play when you are listening to your own tracks. http://www.spotify.com/us/get-spotify/open/

Thanks, for some reason I thought Spotify was like Pandora, a web app.

I was wrong.

Does it do podcasts as well?

If it's in a regular audio format yes. I have a couple LearningRails.com podcasts on mine and they work great.

Clementine, it's derived from Amarok's KDE: http://www.clementine-player.org/

It has the nice feature to queue tracks inside a given playlist ('Queue manager.').

If you want something that approximates iTunes itself (desktop app for managing your library) then checkout Songbird.

I've found this to be very slow and buggy with a large library. Three or four times the last few years I have installed it, again, hoping it would have improved. Then I sit there and watch it hang. Frustrating. Maybe it isn't the size of the library, but the presence of media with non-English titles. Anyways, not worth trying, I think.