I use windows media player cause it looks cool, doesn't error much, and works!
If Microsoft had a dollar for every time someone said that about one of their applications, they'd have 1 dollar
You know, I use WMP 11 on all my computers and I don't have troubles with it. The taskbar integration is wonderful, even though other players have remotes or small skins, being in the taskbar is actually still better(not intrusive into your screen space(meaning it will not cover any data or info on your screen. It is integrated into the GUI, rather than being on top of it)). Also WMP does offer media features(like SRS, Crossfading, Speed, etc.), plus it is a fully featured media player(video and movies as well).
I have a 1.0 GHz computer with 256 Mb RAM and it doesn't skip there.
Winamp is still very lovely. As far as simply a music player goes, that would be my pick then. It is faster since it doesn't have all the extra.... stuff. Not that WMP 11 is slow or overstuffed with whatever, but that Winamp doesn't need all the things WMP has, so because of this it can run faster.
iTunes would have to be a thumbs down for me. Winamp and WMP 11 are very nice, but what really does iTunes offer that isn't in the other two? I don't see how anything in iTunes beats anything in the other two. Yes, it does have that fancy album art scroller thing, but you need an iTunes account to get album art that you don't have(WMP lets anyone get album art). And last time I checked, u needed a credit card to get the iTunes account....
Can't say much for other media players. Well, except in Linux. amaroK(of course someone would say this) is wonderful as far as all Linux players go, and there is Exaile, which I like a bit. Gecko was something else I tried a while back, don't know what has become of that.