With ever increasing download speeds available through cable, dsl, and cellular networks, streaming music has become my favorite way to listen to music.
Pandora (Free, Extra features for $36/year)
Pandora is what I use when I want a "set it and forget it" listening experience. Using what they call the "Music Genome Project," Pandora creates a custom stations based on a song or artist you select. While listening to your custom radio station you can "Like," "Dislike," or skip a song. Over time Pandora remembers the traits that you like or don't like in a song and further customizes your station.
For example, lately I have been listening to "Phoenix Radio," based on the French band Phoenix. At first it was an alright station that played pretty much all tolerable songs, many of which were unfamiliar. Over several days of liking and disliking songs it started playing songs that I listen to and love independent of Pandora, which is sometimes creepy in how accurate it is.
On the other hand if you like too many marginal songs your station can get really corrupted with songs you don't like. My "Passion Pit Radio" station started playing nonstop techno and remixes of the same 3 songs after I liked too many remixes of songs I liked. So be a bit careful with what you like on your station.
With a little investment of loyalty Pandora can become an awesome personalized radio station that only plays songs that you like.
Mobile apps: Available on Android, WebOS, Blackberry, Windows Mobile, and iPhone
Grooveshark (Free on Desktop, $9/month for mobile app)
Grooveshark is my new favorite way to stream music, especially if I want to listen to anything in specific. They have a huge searchable database of music to choose from. You can create a playlist right in your browser of whatever songs or albums you would like to listen to. This is a great way to check out a new album by an artist you have liked in the past, or check out an artist or song that someone has recommended to you. It is also useful to listen to albums that I own, but don't have on my chrome OS laptop.
iTunes has been and probably will be the biggest player in the digital download space for a long time. Personally I am not a big fan. There are other places to download for cheaper and without DRM (digital rights management). My favorite is Amazon's digital download service.
Amazon offers a huge selection of music for digital download, probably just about anything you could care to download. The $.99 al a carte downloads will be familiar to iTunes users but the way I like to but from amazon is through their monthly $5 deals. Every month a new selection of albums is available for $5. This is the best deal there is out their at the moment for legally downloading music. And there usually several enticing offerings at any given time. Here are some of my favorites that are available right now for $5. Amazon offers a piece of software to download and import tracks from their website straight into iTunes. They also have smartphone apps available.