Well my first suggestion would be Youtube, especially if you have a SPECIFIC song to listen to. It's also great for finding similar songs by the same artist.

However, depends just how slow your computer is, I can see how Youtube might now be the best choice.

So I suggest either Sky.FM or DI.FM. Type in either of those like like a standard address (fm instead of .com). Both are sites which have dozens of channels of music. They're sister sites.

Sky.FM is a variety of mainstream stations, their individual channels range from jazz (various types), pop, punk, indie, romantic, top hits (top 40), 70s, 80s, 90s, oldies, classical, piano, new age, world, reggae, country, rock, urban, rap, dance, salsa, soundtracks, and more. This is especially great if you are a jazz fan because there is not just one channel for jazz, but roughly 8 (classic, bebop, bossa nova, piano, uptempto, smooth, etc)

DI.FM (stands for "digitally imported") is more electronic, techno, etc. There are quite a variety of chanel here too, but they're all... electronic, I guess? I'm not exactly sure how to group them in to one large category. Channels here include Liquid DnB (drum and bass), oldschool house, trance (many styles), house (again, many styles), chill, Eurodance, progressive, lounge, techno, and tons more. Most are variations of house. I also found a very interesting "chiptunes" channel - the current song isn't really much of anything, but it seems to be a lot like video game music.

The nice thing about sky.fm is that it has it's own player and you can switch channels easily without opening new windows. Di.fm is still running on an older format that has you pick which format and speed to run it in - not as clean, but might be nice with your slower computer.

Check them out!

(hey, this chiptunes thing is catching on!)

http://www.distortedscience.com/site/wp-content/uploads/2009/10/DI-FM.jpg

I like to use mixpod.com you get to look up music from youtube and basically make a playlist. It's online so all you have to do is make an account and then you can get started on creating your playlists. it's really simple. I don't know if it will slow down your computer, but i have a slow laptop from like the 90's that i use sometimes and i can still listen to music just as well as if it were on a newer computer.

I don't listen to a great deal of websites really because I have such a vast library of music on my computer as is but there is one site I particularly like that plays a damn good radio station if you are into industrial/metal types of music. They actually play a fairly wide variety within that scope but you won't hear say, rap or country on their station.

Website with forum/info/etc:
http://secondshifters.com/
Direct link to radio page:
http://atnevon.swcast.net/

They have winamp, real player and Windows Media Player links that will play without the website even open or a small pop-up window. It should effect your computers run speed at all, though they do have dial-up or broadband options to choose from even when i had dial-up the broad band links ran fine for me though.

I used to use LAUNCHCast, a Yahoo personalized radio player type thing but then it changed and didn't let me do what I wanted to do with it. I then just stopped searching for awhile until my brother introduced me to Pandora. It's easy and free and works wonderfully. All you have to do is sign up (which is free), then choose an artist you like and it will play songs by that artist and artists similar to the one you chose. Or, pick a genre of music, and it will play all the songs within that genre it can think of. There are very few commercials, maybe one every four and five songs and they're never long.

You can also give a thumbs up or thumbs down to songs, which Pandora will remember and play music accordingly. This makes it very personalized. You can also select next, if you don't want to hear any more of that particular song, or you can pause it if you're busy with something else. It's very easy to use--definitely check it out!