MySpace is a great place to hear complete songs without downloading them to your computer. Many bands have utilized this service to bring their music to the fans without having to go through a record label. Artists such as Lily Allen and Regina Spektor built up a huge MySpace following before they ever hit the mainstream. The downside to MySpace is that you need to know which band you want to hear. There are some resources to find new music, but for the most part, users simply navigate to a favorite band's MySpace page and click Play. It's rare that they'll have whole albums up, but there are usually at least three or four full tracks.
Pandora is a great source of free online music that has been assembled using the Music Genome Project. The project forgoes genre classifications and instead categorizes songs based on their melodies, harmonies, rhythms and other musical elements. When you create an account at Pandora, you can specify an artist that you love, and it will play you not only songs by that artist, but by other musicians with a similar sound and style that it thinks you might like. You can rate whether or not you like the songs you're hearing, and it's a great way to discover new music that you might not have heard otherwise.
iMeem is a social networking site that also serves as a way to hear new music. You can connect with friends and listen to what they've uploaded for free. Some artists and record labels use this service to promote different records and playlists, as well. The only downside is that some of the songs are simply promotional clips that are only about 30 seconds long. This can be a deterrent for many people.
Last.fm began as a way for users to simply categorize what they were listening to on various music programs and put some statistics to it. For example, iTunes users could see their most-played songs, their favorite artists, and how those statistics differed from week to week. The service continued to grow, however, and now it boasts a service that's similar to Pandora. Last.fm also offers videos, and it gives users the ability to add information about the artists in a Wiki-like format.
Online radio has become a far more robust format for hearing new music than it was a few years ago. Many stations and programs now offer online feeds, and you can hear anything from a local college indie station to big commercial stations in New York and Los Angeles. Unfortunately, these stations tend to be advertiser supported, and when you listen to a live broadcast you'll be subject to the same commercials as someone listening to the radio in the car or on the stereo. Stations like NPR offer online streaming broadcasts of some of their most popular music shows, such as All Songs Considered. These programs can be a great way to hear reviews of new music.