Sorry it's taken me a long time to reply. I had a serious problem with Windows...and solved it by removing Windows completely! I'm now proud to be 100% Linux!

Anyway, still can't listen to the streams on nme.com! I've tried using KMplayer and Xine in Konqueror as Osbie suggested, and although it does work better (ie. it's faster) it still stops at the end of the first song. I've also tried the link that mma8x gave, and here I get a totally new and, I think, unrelated problem...Xine runs but there's no sound!

But going back to the mplayer problem, I can't help but feel that there's a configuration issue somewhere. The fact that it always stops at the end of the first song, and that it has always done this, even after a complete Suse re-installation or even under a different Linux distribution (I used to use Mandriva 2007) makes me feel that it's not a problem with mplayer or Linux, but due to something I'm not doing. Mplayer (and Xine, and Kmplayer) really seem to think that it's finished it's job when it gets to the end of the first song. One telling sign could be the message I get at the bottom left hand corner in Konqueror: it tells me it's buffering, then it says something like cache fill 4%, and this cache fill will usually go up to 30 or 40%, then start again from zero. After doing this a few times the audio player stops.
I know this is only a small problem, but I'd love to get to the bottom of it as I really love this site, and listen to the nme media player is the only thing I could do in Windows that I can't do in Linux.