If I miss the iPhone for something, it's the iPod functionality, which allows me to carry around a large subset of my music library. Android allows this as well, but there's nothing like iTunes, which effortlessly syncs music over. You rather have to copy the music files manually. Also, this requires tethering the phone to the computer, which feels somewhat out of character for Android as a mobile terminal for the cloud.
My first solution are podcasts and there are some excellent ones out there. KRCW, KEXP and NPR have several great ones. I also love Resident Advisor's weekly DJ sets. But sometimes I'd like to have some more control over what I want to listen to, but all the solutions I found so far, were streaming music, which is not very appealing for me as AT&T's network is not the greatest and, of course, it does not work at all in the subway.
Fortunately slacker.com introduced yesterday an Android app with offline caching. It's $5 a month and it allows listening to several pre-defined "radio stations" as well as define your own one based on specific artists or other criteria. On the phone these stations can be marked as cached and can be refreshed automatically, for example overnight when the phone is on WiFi and connected to power.
So far, my impression is mixed. The website itself doesn't work on Chrome, but it works on Safari. Not a big deal, but it always turns me a little bit off if I have to launch a second browser. The overnight refresh didn't work either: in the morning Android greeted me with the offer to kill the Slacker app, which wasn't necessary in the end. The app itself complained that no WiFi was available, which is a flat lie. Anyway, I refreshed manually, which took almost two hours for four stations, but I hope this gets faster for subsequent updates. There are some other bugs too (which interestingly seem to be typical for Android applications and the way they are stacked together).
The music is so far so good, but I actually like to listen to albums in their entirety, which is by definition not possible on an online radio site. For that I hope we see either Rhapsody (Android app currently in beta) or Spotify (not in the U.S) available soon.