Giving listeners huge listening variety, these providers archive and provide multiple stations. They usually provide a method for selecting what you want to listen to, by genre as well as user ratings. Many are ad-driven, and provide a subscription service that will get rid of the ads.
http://www.itunes.com
You won't get far in an Internet radio discussion without mentioning iTunes. A free download from Apple, iTunes was arguably popularized along with the success of the iPod. While a main advantage of the service is to purchase music by individual song, click "Radio" in the left-side menu to listen to categorized music streams.
http://accuradio.com
"Rock, jazz, classical and more." The interface is a little strange and is ad-heavy, but the broadcasts are as advertised, and a software download is not required.
http://channels.netscape.com/ns/music/radio/default.jsp
Radio by the folks at Netscape. Like iTunes, it requires a software download in order to listen. Plenty of music and talk radio are available.
http://classicalwebcast.com/onepage.htm
Classical Live Online Radio attempts to document all Internet classical music. Lots of classical music links here, both within the USA and as far away as Hong Kong.
http://di.fm
Digitally Imported: Heavily focused on electronica, dance, trance and new age music, and there's nothing wrong with that. And if I had an award for "Shortest domain name on planet Earth", they'd probably get first place.
http://live365.com
Live365 is a major Internet radio provider. They bill themselves as the "World's largest Internet Radio Network". Listen live online, or download individual songs for later.
http://radioio.com
Paid members get better-quality music (categorized by "AM", "FM" and "CD" levels). Windows Media Player gets really messy due to inserted ads, but the music still sounds good.
http://shoutcast.com
Download the required SHOUTcast media player, and enjoy a huge range of genre choices. Good presentation of playlists: You can quickly and easily skim what's currently playing.
http://www.bbc.co.uk/radio
Live radio from the BBC. The interface is a little convoluted, as you must select a BBC radio channel, then a radio genre sub-type or program. But it's very comprehensive, and also has a large database of previously played archives.
http://www.heavy.com
Very annoying interface. These things should be kept simple, and heavy.com is flashier than a Hollywood blockbuster. However, they make up for it with one word: Videos! Note that this is not a dialup-friendly site.
http://www.icebergradio.com
Registration is required to listen. With registration come ads in your email. But there's plenty to listen to.
http://www.launchcast.com
Yahoo Music brings us LAUNCHcast. A Yahoo ID is required to listen. The music can be managed by the Yahoo Instant Messenger, but it's not required - you can still listen via a browser.