For Linux:
I love "DeaDBeef" [http://deadbeef.sourceforge.net/] and "Quod Libet" [https://code.google.com/p/quodlibet/wiki/Guide] for providing the ability to bypass the Pulse Audio Server and playback bit perfect audio via ALSA digital out. IMO, for audio, they are the equal of anything in the Windows world.
DeaDBeeF, a newer project, is lighter on features than Quod Libet, but works flawlessly. Quod Libet has more features and plug-ins, plus the added ability to integrate with the "Screenlets" application [http://screenlets.org/index.php/Home] which provides a multitude of useful desktop widgets, the most significant for audio being "nowplaying".
Edit: I forgot to mention "Guayadeque" [http://sourceforge.net/projects/guayadeque/] a strangely named Linux audio player that's right up there with "DeaDBeef" and "Quod Libet".
For Windows:
I use Foobar2000 and J.River Media Center (ASIO or WASAPI event mode). I give the nod to Foobar2000 for audio because it's free, customizable with some effort and audibly as good as anything I have heard.
On a tangential note, I do wish Foobar2000 would develop a "nowplaying" plugin for the WinXP/Win7 desktop that would allow the player to be minimized, leaving a user customizable "nowplaying" widget on the desktop showing cover art, title, album name, artist of the currently playing track and transport controls, similar to the "nowplaying" widget in Linux "Screenlets". It seems that the free Windows app, Rainmeter [http://rainmeter.net/RainCMS/], can do this, but it requires effort on the user's part.
Edited by Rizlaw - 6/28/11 at 8:43am