Pandora has Apple and Android app versions, and has two subscription options: free with advertisements and a 40-hour cap, and paid.
Pros: We've found the recommendations system works really well, and have even discovered some new favorite bands that way. The service plays you types of songs you'll like in any genre you want, so it's a good way to explore. The preset radio stations are also worth a look.
Cons: Can't control which songs you listen to, which is a bummer if you really do just want to hear one artist or album and not similar types of music. If you listen to the service every day for a while, songs start to repeat, or recommendations get a little wonky (along the lines of playing Disney radio stars near the end of a hip hop mix).
Spotify has free and paid subscription options, and plays through a dedicated player available on every OS as well as Android and Apple phones (with a premium account).
Pros: We have been massively impressed by the sheer amount of music available on this service; Spotify has just about every track you'd ever want to listen to. They also have a really great playlist-making and -sharing setup, which is as easy as copy and pasting a link. Playlists can also be edited by groups of people.
Cons: Obviously being Europe-only (and only Sweden, Spain, Norway, Finland, France, the Netherlands and the United Kingdom at that) is problematic. This worked for us while we were traveling back and forth between continents a lot, because logging in from a European IP lasts for about two weeks before it checks where you are again. Supposedly they're going to release in the US some time in 2011.
There are some other problems with content restriction from record company licensing, and they've recently announced free users won't be able to listen to as many tracks as before, or as many times.
Subscriptions are $5/month for web and Roku channel access, and $10/month for listening through those as well as apps. Users can download songs to the app for offline listening. New users get a 14 day free trial.
Pros: MOG seems to be the best of the Pandora and Spotify worlds; listen to whomever you want and when, and build playlists like Spotify offers, or have slightly-less-accurate-than-Pandora radio-listening options.
Cons: If you're willing to fork out the cash, it's a pretty good deal, but paid still has a hard time standing up to free. Similar artists can be a bit random at times.
Do you use these music services, or any other? Which do you think is the best? Let us know!