You're going to get a lot of opinions about this one. People are fiercely loyal to their media players and their criteria are usually completely subjective. Also, something that works well on one machine might not work as well on another. With that in mind, I would first suggest you get Total Uninstall
http://www.geocities.com/ggmartau/projects/projects.html so you can undo anything you install. Don't trust built in uninstallers.
I use CDEx
http://www.cdex.n3.net/ as a stand alone ripper so integration isn't important to me.
Having said that my (completely subjective opinion) is Winamp 2.95
http://www.winampheaven.net/ (I think that's the last one in the 2.x series). 5.x
http://www.winamp.com/ is nice if you want the newer skins but it doesn't sound any better. Winamp has built in support for most media types and plugins available for almost every other one; a built in radio tuner that sounds respectable on slower modems; skins and visualizations. I think it's the best supported media player there is.
I have also heard good things about Foobar
http://www.foobar2000.org/ , Jet Audio Player
http://www.jetaudio.com/ and Quintessential Player
http://www.quinnware.com/index.php but I have not tried them. There are tons more here
http://download.com.com/3150-2139-0.html?tag=dir .
(I just noticed - 1000 posts. I'd celebrate with a few beers but it's only 11 am.)