Google Music! It's pretty much the music service you would expect from Google: Streaming all your songs from the cloud, once you've told them what you have, and a bit of offline caching.
How do you use it? You use Google's Music Manager to add your songs to the service. It adds play counts and ratings as well. It's a "full featured music manager", so you can search and do all the other things you could in iTunes and Windows Media Player.
When you make a playlist, it becomes ready on all your devices: Phone, tablet and computer. It also has the equivalent of Apple's Genius Mixes called Instant Mix. It works essentially the same way, and makes a playlist out of one input song.
But you don't always have an internet connection, or a good enough one to stream music. So you can either select certain music to cache on your device, and the service automatically caches your recently listened-to music as well.
Google Music launches in beta today, and goes to US users for free gradually (while in beta). You can add in 20,000 of your songs total.
Any Android 2.2 Android device can download the updated Google Music app and get this service (provided you're in the beta).