It's possible that I'm far, far behind the times: but I've just come across
Musikcube, an open-source music player "inspired" by iTunes. It hit RC1 earlier this year, and looks promising in that it combines iTunes-style library indexing (but not file management per se) with support for a wide range of file formats and Winamp levels of system resource use. Subjectively it is no quicker than either of the other players in most uses: but unlike iTunes, it doesn't seem to have significantly more difficulty with larger music folders (up to 51 gigabytes anyway). MC has no video functionality: the trend is towards convergence between music and video players, but personally I find having one application handle both creates more problems than it solves.
Musikcube supports a variety of plugins, although there aren't many available yet. This means, for example, no DSP so far. The project has the potential to attract plugin developers, but I suspect that Songbird will make the running here, since it is linked to both Winamp and Firefox, the two most plugin-laden apps I know of. Musikcube is likely to suffer in general from the greater publicity that will inevitably accrue to Songbird: an open source app without community backing is in trouble.
The MC UI is pretty good, but it has the irritating attribute of looking like iTunes but behaving subtly differently: this means that if you're at all used to iTunes you'll find it slightly counter-intuitive. I do. Meanwhile, it lacks Winamp's superb playlist management/organisation tools and comprehensive keyboard shortcuts. In particular, the "randomize playlist" function - as distinct from "shuffled playback" - is sorely missed (EDIT: mc does have this function after all, it's just in a stupid place). Shell integration is essentially non-existent in MC too.
If you're like me, you've been wanting to move to iTunes for some time owing to its UI, which is far slicker in normal use than Winamp's, even though Winamp strictly speaking has all the same features. I've been held back by iTune's lack of functionality, principally its inability to handle ogg and FLAC files, and to a lesser extent other formats (mpc etc). My hope is that as MC matures, it will address the issues I have mentioned above, in which case only an equally mature Songbird will be able to compete with it, since Winamp development has essentially ended and Apple's design approach runs counter to every nerd bone in my body.
If all that sounds like an endorsement, then I suggest giving MC a go.