Google Music (Beta) program and I asked to be a beta user. It was something of a pain to set up, because at the time, Google had not worked out deals with record labels to allow them to distribute central copies of MP3 files based on some evidence that you already own that music (Apple is doing something like this with their iCloud service). This meant that I had to upload all the music I wanted to have out there, and it took some effort and several days to do this (their music uploader application has since improved so this would be easier now). But I ended up with 19,767 songs on Google's server (it's free for up to 20,000 songs).
This is nice, but in practice it was not very useful because all these songs are also on my PC (on an external drive that I travel with), so it's easier to play them in iTunes if I'm using the PC. I didn't worry about because I thought that Apple's then-coming iCloud music service would solve all my problems since I'm an iPod and iTunes user anyway. But when that service launched, it wasn't as good, easy, or cheap to use as I had assumed (long story).
Cut to the chase, Bruce: I just discovered that there are several Google Music "client apps" for the iPhone and iPod Touch that allow me to access, search, and stream music from my online Google Music collection. I installed a free one called Melodies and it worked well on both wifi and on 3G on my wife's iPhone. So I spent 99 cents to upgrade to the "pro" version, mainly to get the shuffle feature.
This is really great, because even though I carry 4000+ songs on each of my two iPods, there are times when I want to hear something obscure that I haven't bothered to copy to the iPods (where I need to save room for recording and other apps). Here's a more detailed review of the Melodies app.